From mboxrd@z Thu Jan 1 00:00:00 1970 X-Spam-Checker-Version: SpamAssassin 3.4.4 (2020-01-24) on inbox.vuxu.org X-Spam-Level: * X-Spam-Status: No, score=1.2 required=5.0 tests=DKIM_ADSP_CUSTOM_MED, DKIM_SIGNED,DKIM_VALID,FREEMAIL_FROM,HTML_MESSAGE,NML_ADSP_CUSTOM_MED, RCVD_IN_DNSWL_NONE,RCVD_IN_MSPIKE_H2,T_SCC_BODY_TEXT_LINE autolearn=no autolearn_force=no version=3.4.4 Received: (qmail 3958 invoked from network); 9 Nov 2023 19:12:29 -0000 Received: from mail-me3aus01on2105.outbound.protection.outlook.com (HELO AUS01-ME3-obe.outbound.protection.outlook.com) (40.107.108.105) by inbox.vuxu.org with ESMTPUTF8; 9 Nov 2023 19:12:29 -0000 ARC-Seal: i=4; a=rsa-sha256; s=arcselector9901; d=microsoft.com; cv=pass; b=lhDJnQT1lwNajuEcNG4mq2iPJfSWRT9FkbbbSpNsUGvt1rE+aFghsUiJFMuUbm4olbaojNV6Vuc3VqJcrAvv1weJboHteX/Vs5jb1h+TTSqdYu5ASvteLUYAGDwYYRJh9KqHuYGG3JmZTKDE44Nly7Pt67+5LfkyndlEz2D0sg9MnPWvyVF28SOpeZ5vvmzUSHpTA5wqSQbfCAkVSaAgoptB4LnLdG9g/0e1yMzkuoZ4RprbMR/NH7C3Qn1e2fOFxAfqV5qdgV8yzQEOvsHQ3jIJPWEuHsSs5skfmluxZkkpaGo6GtAMNSaHUWLsK96GoGNhinq0erpO+Xatcr8XtA== ARC-Message-Signature: i=4; a=rsa-sha256; c=relaxed/relaxed; d=microsoft.com; s=arcselector9901; h=From:Date:Subject:Message-ID:Content-Type:MIME-Version:X-MS-Exchange-AntiSpam-MessageData-ChunkCount:X-MS-Exchange-AntiSpam-MessageData-0:X-MS-Exchange-AntiSpam-MessageData-1; bh=fOXfJDe4ax1z6DM3iHAeI2NZoAZ7cO41oGCy70+m/oI=; b=SRdPYbkwcnjtBJ/b8x1P+eMD5bNPLwNLaet0ukqh00GSL1aEEl1Cp/ygJD+s81vqQQ0RbIvnTCoTFpuWlxwrS33HJp4qXirmlldE4fS4YiDULcYNWwy0Gb1h1jQb4DmEEb+oBmlJHqFXGNLySM7mDDr7XDArh6CMceI0Tl3nBKQBrP9iVxMl2UZJhM23xZelMzH5d5CRTItmYDpS8vjU+CrVOTd1XM8uLk6jvHXOG40hPP1aygRhGthFzTBgaNPoCL/mCCQTfSP+7aWOeATCd+bI92xSFKBpRIByhPdmHfK5nm3HmwZQGy+IYa9wKJEe8euo4z+cAsp7SMobxRWlxA== ARC-Authentication-Results: i=4; mx.microsoft.com 1; spf=pass (sender ip is 209.85.222.51) smtp.rcpttodomain=mq.edu.au smtp.mailfrom=gmail.com; dmarc=pass (p=none sp=quarantine pct=100) action=none header.from=gmail.com; dkim=fail (signature did not verify) header.d=gmail.com; arc=pass (0 oda=0 ltdi=0 93) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=groups.office.net; s=selector1; h=From:Date:Subject:Message-ID:Content-Type:MIME-Version:X-MS-Exchange-SenderADCheck; bh=fOXfJDe4ax1z6DM3iHAeI2NZoAZ7cO41oGCy70+m/oI=; b=dxtbDWwsePefdvjyXMEqekzcZszVQ2QZ5IU9l5zbcLwo2HUwC0wONFmeCY/CGYkZH7GefV8pha4V/jhwATHjP+MHZvIxkeBzQ6ouPb4WWhQZSRCx2gJz/gxrJGFlw2uzOEI33nahogJnYBKsosa+mrqKiXAeD6rzOQpSThsspHnCUFr0IWy8U7GC5Z56In36YzB5+oSso/RFYE7YSEjRRg07RDC3PvjREgeQkUASVbWpMbHqJgHpiO0/mz7cHewhACWFWmNw18I1bVdt0BvXdA+/ejy1JCww8XRwZQaCfDsQ+0qMc+UM1jBhLjJyzAnMCSvfWz0AyjoPWs6lQEceoQ== Received: from SmtpServer.Submit by SY4PR01MB6624 with Microsoft SMTP Server id 15.20.6954.28; Thu, 9 Nov 2023 19:12:24 +0000 ARC-Seal: i=3; a=rsa-sha256; s=arcselector9901; d=microsoft.com; cv=pass; b=ORLboQd65J3dY5w4LFqVx2nzJtYw7yJiTg100/pslBUNxvnTz1mcelLV0SLQnLqjxoFqGKQtlQ8m0+P+/jssXWHra3khjtU7FB77Qk3Ghm0zYfpY3kqGsG6tpSLa1VbGx7YVpzi3HmSuwETQMOtZzPIAWFFZQwK0w1smpFY6jFN1t4TjgI6U/DxlOyjlpsRGBv0pLuO7fwBwV8zHUu/DbO74oNb/OHdk1qOiXb69juY0iOqKhYVjfXjyWHtj7zjB6AEWS8DbJ8tBxBrevNs7VNTYM1POM/tWM8uq/hhmlqfNWhAv/s5UJ/6MItWnSVfsOYcfgzrY8axoHhWFRRFtMg== ARC-Message-Signature: i=3; a=rsa-sha256; c=relaxed/relaxed; d=microsoft.com; s=arcselector9901; h=From:Date:Subject:Message-ID:Content-Type:MIME-Version:X-MS-Exchange-AntiSpam-MessageData-ChunkCount:X-MS-Exchange-AntiSpam-MessageData-0:X-MS-Exchange-AntiSpam-MessageData-1; bh=UA8oGm8Wf/vfmiKSyGKa/BKF/cYA36Ud8Cdr1gdGEs4=; b=f4/iuONRmGFA51J0yy4TfNfnZFI4Eipxm4D9edKWzTy+J9wN6Fxpv/YnHE0HTRcd7QBVwUAhI31MkI2Gcu2Y1e4MAG1sWc7U9yfdWup4KPxdxgH7erMJqYhOO2lXTIfdSAYCs2fki3fhqTmixtJX+y4ySKCvPEizf6DH2tNyjEcNtwuOlsihocqoxtJVnZxoykZz0JdxdtvHz5bPwd3d2RGZM5MNP116EmuUFG896wnSUKmjkVF5KMc+mh2cKNmL/IoRhj5bqf8QFnSxhDSu5LKwpfr2Zvv4ANCVlygPxYwhr/O/2SaIurCvgpzPR2xAt2s2+3RwYNqaYGN9oPuwxA== ARC-Authentication-Results: i=3; mx.microsoft.com 1; spf=pass (sender ip is 209.85.222.51) smtp.rcpttodomain=mq.edu.au smtp.mailfrom=gmail.com; dmarc=pass (p=none sp=quarantine pct=100) action=none header.from=gmail.com; dkim=fail (signature did not verify) header.d=gmail.com; arc=pass (0 oda=0 ltdi=0 93) Received: from MEWPR01MB9021.ausprd01.prod.outlook.com (2603:10c6:220:1f5::18) by SY4PR01MB6624.ausprd01.prod.outlook.com (2603:10c6:10:133::6) with Microsoft SMTP Server (version=TLS1_2, cipher=TLS_ECDHE_RSA_WITH_AES_256_GCM_SHA384) id 15.20.6954.28; Thu, 9 Nov 2023 19:12:18 +0000 Received: from MEAPR01MB3654.ausprd01.prod.outlook.com (2603:10c6:201:38::9) by MEWPR01MB9021.ausprd01.prod.outlook.com (2603:10c6:220:1f5::18) with Microsoft SMTP Server (version=TLS1_2, cipher=TLS_ECDHE_RSA_WITH_AES_256_GCM_SHA384) id 15.20.6977.18; Thu, 9 Nov 2023 19:12:15 +0000 Received: from MEAPR01MB3654.ausprd01.prod.outlook.com ([fe80::ffef:afb4:6a8d:9649]) by MEAPR01MB3654.ausprd01.prod.outlook.com ([fe80::ffef:afb4:6a8d:9649%3]) with mapi id 15.20.6977.018; Thu, 9 Nov 2023 19:12:15 +0000 ARC-Seal: i=2; a=rsa-sha256; s=arcselector9901; d=microsoft.com; cv=pass; b=O6YpcZ1Dw0GTIeV7dnZ/hj3115JuEb9hPwZ7G0zaFFNRw5RfogF8CBmApL/JTPHxmqxIa9OXFjI0xXa0w2YbYJO4PfFtBBeiGhqjEKK5NrrSTFjuQUG/l+Pck+bYN64SM0Xl/kYYiX3bZEk82f15CMSLH0akc6bQSpLUYrbiVIMgKDPl05DKRltWQnJ01uRFjmAU5euDtlWe/iRCP1lqG1sz1AZQgbyiiAaRkiQVsZE+N+QotB6L5bz7JWmnciqKHd3YzbgOYqPEcKq7gWOHFaXe7T4pnYW2pJylHUlRPL9G5J8B85EoSCLQ1QgWtIIBb3TbDkfOeEwMgRbwU1/FFA== ARC-Message-Signature: i=2; a=rsa-sha256; c=relaxed/relaxed; d=microsoft.com; s=arcselector9901; h=From:Date:Subject:Message-ID:Content-Type:MIME-Version:X-MS-Exchange-AntiSpam-MessageData-ChunkCount:X-MS-Exchange-AntiSpam-MessageData-0:X-MS-Exchange-AntiSpam-MessageData-1; bh=UA8oGm8Wf/vfmiKSyGKa/BKF/cYA36Ud8Cdr1gdGEs4=; b=TLnnTbTVmmqeaeQM2qFRWQncbF1y9cjL0g+Fj9i6RMjHcwYhdV/PCULceGSdkYcYYyosH/GCKp4bDuxBQeFJpzkdr0aI0XzdUjUyuzYrHW/PZdiXmmkd4g664Lt+gB9CIV7qyD6P6dOC3htPoPBW0fWUfKP5P3ZMnZERpygj+tmytmGPfvqV0lwi+fVkjDC+kSDeF96CZUBqPvY/Y/vfKah6/7PV9pAKv78FcbIfOftB+327VEE679BQHb+rM/ZPSDKLEoRiTk8JiVt7h+Zv2pqZNeEaJwE9hJz1W31yyeQBD6XI/j8w1aT4aOf1kS97iC0w0DDnC28QbIKVuVZ+aQ== ARC-Authentication-Results: i=2; mx.microsoft.com 1; spf=pass (sender ip is 209.85.222.51) smtp.rcpttodomain=mq.edu.au smtp.mailfrom=gmail.com; dmarc=pass (p=none sp=quarantine pct=100) action=none header.from=gmail.com; dkim=fail (signature did not verify) header.d=gmail.com; arc=pass (0 oda=0 ltdi=0 93) Received: from SY5P282CA0077.AUSP282.PROD.OUTLOOK.COM (2603:10c6:10:201::15) by SYZPR01MB7366.ausprd01.prod.outlook.com (2603:10c6:10:177::11) with Microsoft SMTP Server (version=TLS1_2, cipher=TLS_ECDHE_RSA_WITH_AES_256_GCM_SHA384) id 15.20.6977.18; Thu, 9 Nov 2023 11:47:30 +0000 Received: from SY4AUS01FT006.eop-AUS01.prod.protection.outlook.com (2603:10c6:10:201:cafe::c9) by SY5P282CA0077.outlook.office365.com (2603:10c6:10:201::15) with Microsoft SMTP Server (version=TLS1_2, cipher=TLS_ECDHE_RSA_WITH_AES_256_GCM_SHA384) id 15.20.6977.19 via Frontend Transport; Thu, 9 Nov 2023 11:47:30 +0000 Authentication-Results: spf=pass (sender IP is 209.85.222.51) smtp.mailfrom=gmail.com; dkim=fail (signature did not verify) header.d=gmail.com;dmarc=pass action=none header.from=gmail.com; Received-SPF: Pass (protection.outlook.com: domain of gmail.com designates 209.85.222.51 as permitted sender) receiver=protection.outlook.com; client-ip=209.85.222.51; helo=mail-ua1-f51.google.com; pr=C Received: from au-smtp-inbound-delivery-1.mimecast.com (103.13.69.101) by SY4AUS01FT006.mail.protection.outlook.com (10.114.156.122) with Microsoft SMTP Server (version=TLS1_2, cipher=TLS_ECDHE_RSA_WITH_AES_256_GCM_SHA384) id 15.20.6977.19 via Frontend Transport; Thu, 9 Nov 2023 11:47:30 +0000 ARC-Message-Signature: i=1; a=rsa-sha256; c=relaxed/relaxed; d=dkim.mimecast.com; s=201903; t=1699530450; h=from:from:reply-to:subject:subject:date:date:message-id:message-id: to:to:cc:cc:mime-version:mime-version:content-type:content-type: in-reply-to:in-reply-to:references:references:dkim-signature; bh=UA8oGm8Wf/vfmiKSyGKa/BKF/cYA36Ud8Cdr1gdGEs4=; b=Y+woMk8dtYHs9Ed4fULy5oW5Vv2Nn82hb9k1dNWzO0yAHX5nc8l9tBJkd5uUvHbWyAqyk/ VTyticcY7ocfo2D+dy6EO1IYBHQqdP3gdL7vYnDsl7GS9r/SFxcqD6ZleAJe1pxKQ209Yy fyHV9hQPQimqqKzbWXYcnlnr1K+CDi/YJCZFyILmNmnRJHrs6Os1dRQrHX3WRw2+RSYhUG cvwnqQA/y3j0SyEYMZlwQEkbd66+BDa+caGqwA+SCYOuLPE10UcXY+JU6zffMcnFq+vtq9 baOPCu71H8+BarfSob7JuV+pacjHycAAW1hSS70fZCf+6OwufjXVxeCuRYUROA== ARC-Seal: i=1; s=201903; d=dkim.mimecast.com; t=1699530450; a=rsa-sha256; cv=none; b=Kz3ckCCv1t+DZmbs0ZM4z1csh5YepzInwlznlAVUrJ44H4+W/nyNFyq8i7anqVcp08FXQG 8fcmgJR+0Bissx5jrdnwYfuBb/Um/uLdhNggxv34Zjk9vK/iDSM4rGXjl0y6+8hwQOnPVK wlxgDaOMEmBBrS4mgOo0bjYz1qzDuM/nLK2qWoivdVnI7ZzJpyfoe5QHIH+WYQNMlIXWnA Oe9ef/NxLTzJQANcTKZQVew6vztJnYbLb3bXl291xPVt1SBh9ciBL4sU2dQJTEg/77RwZT ZwwttcCYU6FAxZzwQIsJB83qPkMiG2pVp0wy3phXHzR7OC8jJcoKsYaIdPZRxg== ARC-Authentication-Results: i=1; relay.mimecast.com; dkim=pass header.d=gmail.com header.s=20230601 header.b=Vd5pj7CL; dmarc=pass (policy=none) header.from=gmail.com; spf=pass (relay.mimecast.com: domain of posinavrayudu@gmail.com designates 209.85.222.51 as permitted sender) smtp.mailfrom=posinavrayudu@gmail.com Received: from mail-ua1-f51.google.com (mail-ua1-f51.google.com [209.85.222.51]) by relay.mimecast.com with ESMTP with STARTTLS (version=TLSv1.3, cipher=TLS_AES_256_GCM_SHA384) id au-mta-107-eTqJwePKO32lGMf1Ym2t6g-1; Thu, 09 Nov 2023 22:47:20 +1100 X-MC-Unique: eTqJwePKO32lGMf1Ym2t6g-1 Received: by mail-ua1-f51.google.com with SMTP id a1e0cc1a2514c-7bac330d396so304505241.1 for ; Thu, 09 Nov 2023 03:47:19 -0800 (PST) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=20230601; t=1699530438; x=1700135238; darn=mq.edu.au; h=content-transfer-encoding:cc:to:subject:message-id:date:from :in-reply-to:references:mime-version:from:to:cc:subject:date :message-id:reply-to; bh=e9Ao7zFg78yIS75R8UG8X2I2SBTFc/drUR/AACPPQuo=; b=Vd5pj7CLWluXAHJkgfPR4Co+IzVz54CXry4ijokuZMmkrY3JV94dUM/9++wws2iPRk by9STnNsdAuGlaOfAvCo3d1DWElhCab3ndxrhjaPJJo3AtYtyH/Jr6ujN/v27bFI2BYX EjiL4F1M7lFLqftrOuIxEK0DGW920sgVNuWzlZZ2vEhq4ox3YTaaqMUB0Puz2TZ5/qnk B8cQdr9BhjwPRJIdi2Tz3v55279lZKZUefNpsqKqoUd0xJrCvGtdVju0DkGvo+Rg4FA6 dVZTD7QWuCJx7RQRUbBdko/spqbn+rIwdMKI7gi0sWOEQF+Rq1l9Mew8VcVyti8KlLlN xfvA== X-Google-DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=1e100.net; s=20230601; t=1699530438; x=1700135238; h=content-transfer-encoding:cc:to:subject:message-id:date:from :in-reply-to:references:mime-version:x-gm-message-state:from:to:cc :subject:date:message-id:reply-to; bh=e9Ao7zFg78yIS75R8UG8X2I2SBTFc/drUR/AACPPQuo=; b=T3CZRBDM7+xWaKYqY5nsh41QdD6zT9w//xqxcTYPgWSUylx9h8Ot/EIQjpFwZuZ9a3 EUhiyKiHvcTBHp7nThgXa83iTCzbSpNCWH0++Zay9jJVXE9yxjgEeDCsk9ngVMClUQ28 c2Bxs7BOmK6Qxtj/gT/pmWanXxSA1RH0fyp8wSz0t0Kw6ToVp2If7As+7fHwSEm5UxIy y/P+AigUO9Mq0/vr/NmnLPtTcDYc0YxGzHnBomSf1gY40eoauhKS2jEPM+JG2YM7UxhN CJLQiPkwvQE7WY1FedHQz9tnCHxlh1UzXg4mzpI5umR8071QBQSqpvHIyQDU777LVhnI vz9g== X-Gm-Message-State: AOJu0Ywkt6hMiI5o6Z6KFArRs/lh1iXSK0n1wHX3MvK6prlLwS4skS9m kXf7CUx+Fv+wZIea3v41/GKYS37gFjqAZERKmIw= X-Google-Smtp-Source: AGHT+IGyuCCfA1CxL7zmfjXaj9OmXLdl5OLZ7AX9e0J8ODUcEJxLgXPZ9nNFaI/3Ai4Hql5Ga7hmeqCsUiosouMUh/g= X-Received: by 2002:a67:c213:0:b0:45d:9fa9:fb1f with SMTP id i19-20020a67c213000000b0045d9fa9fb1fmr4359188vsj.35.1699530437478; Thu, 09 Nov 2023 03:47:17 -0800 (PST) MIME-Version: 1.0 References: In-Reply-To: From: Posina Venkata Rayudu Date: Thu, 9 Nov 2023 17:17:03 +0530 Message-ID: Subject: Re: The game of the name: Standard constructions, triples, monads, fundamental constructions To: Urs Schreiber CC: "Michael Barr, Prof." , "categories@mq.edu.au" Authentication-Results-Original: relay.mimecast.com; dkim=pass header.d=gmail.com header.s=20230601 header.b=Vd5pj7CL; dmarc=pass (policy=none) header.from=gmail.com; spf=pass (relay.mimecast.com: domain of posinavrayudu@gmail.com designates 209.85.222.51 as permitted sender) smtp.mailfrom=posinavrayudu@gmail.com X-Mimecast-Spam-Score: 0 X-Mimecast-Impersonation-Protect: Policy=MQ - Tag Header Only on Default Settings;Similar Internal Domain=false;Similar Monitored External Domain=false;Custom External Domain=false;Mimecast External Domain=false;Newly Observed Domain=false;Internal User Name=false;Custom Display Name List=false;Reply-to Address Mismatch=false;Targeted Threat Dictionary=true;Mimecast Threat Dictionary=true;Custom Threat Dictionary=false Content-Type: multipart/alternative; boundary="MCBoundary=_12311092247270011" Return-Path: <> X-EOPAttributedMessage: 0 X-EOPTenantAttributedMessage: 82c514c1-a717-4087-be06-d40d2070ad52:0 X-MS-Exchange-SkipListedInternetSender: ip=[209.85.222.51];domain=mail-ua1-f51.google.com X-MS-Exchange-ExternalOriginalInternetSender: ip=[209.85.222.51];domain=mail-ua1-f51.google.com X-MS-PublicTrafficType: Email X-MS-TrafficTypeDiagnostic: SY4AUS01FT006:EE_|SYZPR01MB7366:EE_|MEWPR01MB9021:EE_|SY4PR01MB6624:EE_ X-MS-Office365-Filtering-Correlation-Id: 1ab7c3dc-cf97-4674-6b8c-08dbe119a7b4 X-Moderation-Data: 11/9/2023 7:12:13 PM X-LD-Processed: 82c514c1-a717-4087-be06-d40d2070ad52,ExtAddr,ExtAddr X-MS-Exchange-AtpMessageProperties: SA X-MS-Exchange-SenderADCheck: 0 X-MS-Exchange-AntiSpam-Relay: 0 X-Microsoft-Antispam: BCL:0; X-Microsoft-Antispam-Message-Info: =?utf-8?B?RktZZjJBYlFMcjNVUFlER2VJc004Tm9HNHhKOUt4MXJlcDFiSkVvc1dHS3hw?= =?utf-8?B?QW5wdTRrYzdQbjFrSkRLSktEL2NBTXFtajFDbHRsOTlvSTQ0L2pRT29nR0RK?= =?utf-8?B?MWJabXQ2ODdXNTlqK052d1JZemlIckhhWThvSW1TLzdjQmgzYzVIUFZpU0p2?= =?utf-8?B?Z1gyM1lnTlgzQ29wUGFOMmhqTGNtY3o0N3VnUUdSb25JRXU0akU0ZmMxTFdN?= =?utf-8?B?Nk1uMTZvUFFvalVRd2VoM1VwZkNNb0ptMzVjSjc1OWc5R3BzSlN5dXNmY0NJ?= =?utf-8?B?TUZNMWxoNm9weE1ibnZkVVZHZWQ4R25IemF1bnhmNVFDcVRCeEgrNDlVa3ZD?= =?utf-8?B?V2ZtWVdOUkpsbU10UFVJaTNOQVRaamZjUlBtajlSV1FqRldGZlNadmhlMHNw?= =?utf-8?B?R24yNy9uMHRvaW1hNlBiTVZYbUJDM0lLWjhlVzAvUzM5RW1WaENBZE9DZE9h?= =?utf-8?B?MFRRelFPOXJ2S1Y0VE1UQ3dCU2JxUFFoVUI4TVJnbmd0UnpHL09qSk9CV2E5?= =?utf-8?B?dk1BZGVWSE5GVWhuWXBGUy9kNnMrZ2JYdjZjTVk4NVdvY3BEdXJvQnlENVVt?= =?utf-8?B?UTZURTcyUGlRSG5qZkpsdVR4NjcwK2tNUnVzaE9DMTBtQWc2WVlvQ0JMSWtZ?= =?utf-8?B?MkwzcXEwaCsrWTB5bzNmdTkzSTBtSkpnUnlyWHBzUmQ0Y0V5elVnYjdSTFFF?= =?utf-8?B?dEZ2V2VlU1d3TWUvdm8veExWRlpxczlDbXc0WkprWUdORjlnenZ0TVFnVG42?= =?utf-8?B?aVIvUGhBS0hJdnlaNHlubU9JUWpHWDN6NnJuZktKRTZJVUJ6K2VZY1Q2UG9Q?= =?utf-8?B?MmhvZi94aFArWTFjQlQ3MTZvR204ZW1jRWRpcUd3TEt3K3ZMY2djbk5TeS95?= =?utf-8?B?VUZxZVAyQ3dUNlcvMi84U3Fnc3NXRytBWURhZERuZjIrTXZwajhXc2F5aitG?= =?utf-8?B?UkZ1Rjd2SFZkVnMrT3plek9YVDkycmc4NS9UdEl4ZlpZR2lsNGt4UTVZdElZ?= =?utf-8?B?aGVYRTR4VXZjZ1VkWkFRT0h6M0FaN3M4S0pVbFZOWndJNVNPMU93Rm4wY1Zp?= =?utf-8?B?UEtZS1NIYm5hYWxaS3BNa2ZpRm56dEFONGlKaHJja1daa1Vkc3hKTkJ6WkRO?= =?utf-8?B?Wkc3dTZMTXU4NkNDNk9aazJQSnNOTExnWWovQm5BVCtrSlpSN3BnZGp3anRD?= =?utf-8?B?cGdMZXpUN01rNnF0S0JEQVBxdUFEYlpTaXFpU0NXMkVSbWFlOFlOT0g0cUlJ?= =?utf-8?B?UDNpVFpxWkhCRFZHR2gxWUFCZ1diVm45Sk00Wk1IcTh3OHRVdz09?= X-Forefront-Antispam-Report: CIP:103.13.69.101;CTRY:US;LANG:en;SCL:1;SRV:;IPV:NLI;SFV:NSPM;H:mail-ua1-f51.google.com;PTR:mail-ua1-f51.google.com;CAT:NONE;SFS:(13230031)(4636009)(136003)(39860400002)(346002)(396003)(376002)(8000799017)(64100799003)(82310400011)(451199024)(48200799006)(1800799009)(40470700004)(2906002)(54906003)(6666004)(53546011)(33964004)(32850700003)(498600001)(89122003)(88732003)(45080400002)(76576003)(966005)(82202003)(73392003)(7416002)(8676002)(70586007)(66574015)(26005)(7366002)(5660300002)(41300700001)(7406005)(7336002)(7276002)(68406010)(786003)(6862004)(4326008)(76482006)(8936002)(32650700002)(42186006)(83380400001)(336012)(316002)(82740400003)(156005)(166002)(55446002)(7596003)(86362001)(7636003)(30864003)(35950700001)(5930299018)(40480700001)(40460700003)(43620500001)(15398625002)(41080700001);DIR:OUT;SFP:1102; X-Auto-Response-Suppress: DR, RN, NRN, OOF, AutoReply X-MS-Exchange-CrossTenant-Network-Message-Id: 1ab7c3dc-cf97-4674-6b8c-08dbe119a7b4 X-MS-Exchange-CrossTenant-Id: 82c514c1-a717-4087-be06-d40d2070ad52 X-MS-Exchange-CrossTenant-AuthSource: SY4AUS01FT006.eop-AUS01.prod.protection.outlook.com X-MS-Exchange-CrossTenant-AuthAs: Anonymous X-MS-Exchange-CrossTenant-FromEntityHeader: Internet X-MS-Exchange-CrossTenant-OriginalArrivalTime: 09 Nov 2023 19:12:15.3474 (UTC) X-MS-Exchange-CrossTenant-MailboxType: HOSTED X-MS-Exchange-CrossTenant-UserPrincipalName: qH+HAoUW6hce6Vp5sqrF3KF7psJXZRULB9IhgqythtgkGdvB4VhhzgFIe27nKiavtgYwbYkH2LgywH8Q864xFSVGZ88a5bAFvqNEIKOdVTI52hQ7WtRXxZPmhW3ofrGtF4gG4OhFEJNyo4EVJXxVL6eMq32xtv9S2TJ3Fk4OUWFQlGORt/SsvwoQZmS1J/tv47GIGuMS8lqdY412RTBjfh/QYnh+/t4QMx4xdyZMmX0= X-MS-Exchange-Transport-CrossTenantHeadersStamped: SY4PR01MB6624 X-MS-Exchange-UnifiedGroup-DisplayName: Categories mailing list X-MS-Exchange-UnifiedGroup-Address: categories@mq.edu.au X-MS-Exchange-UnifiedGroup-MailboxGuid: 9c2f954e-92a7-451b-b723-a07075d7adb5 X-MS-Exchange-UnifiedGroup-CustomizedMessage: RedeemedBusinessGuests X-MS-Exchange-Parent-Message-Id: Auto-Submitted: auto-generated X-MS-Exchange-Generated-Message-Source: Throttled Fork Delivery Agent X-MS-Exchange-AntiSpam-MessageData-ChunkCount: 1 X-MS-Exchange-AntiSpam-MessageData-0: =?utf-8?B?ZTgzS0FMM0VEUHpJTlFHRkxTNEFGV3FWOWpNVlc1aW55WC90NXVDM0hVeURF?= =?utf-8?B?SnZwU1VTZ0VLb1pXeUhjOHdzMDkzQjlqRzFJNUdFWlNjL2FudDRFbEk3TmNq?= =?utf-8?B?d051ZExPczJ1b0ZaVXIzVUsyTi9ZcHp4OU1DVlJRVllaNFNFSHZUQ0hkSGpI?= =?utf-8?B?VkVsNjdLTEVRaU8xc2RjYjAvMGw4MmdpalZWR0Uzcm1MczlobUFEQWMvZGhx?= =?utf-8?B?VG82Ui9VVDlNUzZMUlpLbUpQTXVBL1BmYVgrTGNaUmJhb2dtalVPR3oyeDl4?= =?utf-8?B?Uk84WE50R3ZMVXNMbVBkS0pUbHJHN25lRlg5ZE5rbmNjbXIxWmdnd2I3ZHFM?= =?utf-8?B?NkR0ek5IRlNlVDZzeitucElYRVhhNzYrbk1wWUFoSVlzeFZJYmg0ZkpXcEds?= =?utf-8?B?ZU1MZ0kzQkJucDRBczZiaFBrQUVRUEJBTGJyeHVjQmI1NG1oL0FmbW1RZEhk?= =?utf-8?B?SFljeGJ1VWE0QmtoYlRQeU5taU5TNmF3TnRSZmlteHIySnUwTGx2VkJPQU1Y?= =?utf-8?B?UnFDaHg5cXhCa3FGeXpuL09Ua0JyblZRTmZNMTJwYUdGRzI3NXRRQmpjb3VD?= =?utf-8?B?SHY4dmdsdWkyV0ZsUjB4empmNTJtSWFQNjJCSW1XNEx6ZGZheUN4K0x0clZL?= =?utf-8?B?dXZ2cTlBbU03Ly9aa3lPTEVENkdoVkQxN2JvRjRrWmJIckFkQ2I1anZnTmpq?= =?utf-8?B?MDBRSWl3VVk3bVlxKy9oMmViZndPTVpnZTlJeHlNdXUrWnpzYVA5VUsxOUsw?= =?utf-8?B?TVZ6V3dWQzNOa21GNDdRUSsvSTJMR0R6aDZLbEh1MG9kMWlNMW9aMVVTdE9D?= =?utf-8?B?cTRnU3AyQmw2ZERETjN6THE2bVp2NUNwbmcyZHZGcWJRd3Q3aGl2aVpla1pt?= =?utf-8?B?SytxMVVodERVRDAwN3VuQTg2NWtmMEprN3F1YjZqRjU3WWVGQVVzOGhQTkpK?= =?utf-8?B?WExzekhHazdrcHNJMENKSTNBNlpaelZFNDlDbUpOWStIa3VJbWFUeXNUU0ZI?= =?utf-8?B?VCtlbVB1RUxxZzZka1NBTTFkQ1hMSHo1VEVvckdQbjFxVXp0Tk5xTTJNNHhp?= =?utf-8?B?MG9rQnJvSGdkUmVqdG5UbWp5TFQrVlBpdUE5K2d0ckRId0czU0ZHWjBCdzlZ?= =?utf-8?B?ZGhORXl1UmRkeFJMMnMxMHlDc1ZvTkgzRUkxSHpZdFV6WWxMdUNPWFhHN1hN?= =?utf-8?B?YWh2UWVLdnNZZ1JaL3dYTE5DcEhaeVpteCtMSTRsMlNKY3FPaTdVVUdCWE1l?= =?utf-8?B?SEIvdWMzQTc1ZWxEd21LQ1psRTRwUTUxV0kwWmhSOHlXSnVNNGJoSDh1Ukxi?= =?utf-8?B?aFRnY2RTdjZKYTA0ZVZlSEtodFQ1a2lJemJRRjMwVEJKajV5WGpWMTN4ZmhB?= =?utf-8?B?OThtUnQxRjdkYXM1ajc0b2FIOEFRcGRpdmJJTE9yVmhScGhlTENLZDVRa2t2?= =?utf-8?B?ZVhVYjluaFJPZDlYa2FHYXptWGY2bkY5YlJBaDlPN1dLMFBsbjZqajRQR1J4?= =?utf-8?B?QXhFWmdIWXJHVXd0azRtaHhKd1dqOUxyOG5IdnN0ZVV3WE5DSDc4emE0cU52?= =?utf-8?B?M1NPSndVWGMxTW9oK2xmRWZ1QTJZTGJETkpPSnk2WXlEWXVVbmZJV2l0MkJq?= =?utf-8?B?bkExTnc2MFh4SGJZbStGQWRCNmVIY0p5dDhCaHUzVTVZdzNMay9qczFReE0v?= =?utf-8?B?ckh3K2hmWHVObDFvbmowOEJkTnd6NDVtLzJSUWxmTVZGMFoxN0dHQTBmMTUv?= =?utf-8?B?ajdSMGlodzVFaU43TWF0enhEckE4RHVrcjRzaGxUeDVJWHNiWVU5VCsxY09W?= =?utf-8?B?QUQ1aVIwNXVpVVlqUzF2WVBCZnV3SVNDQW1UNlZtbDFWRk5JSS9DTEJvNnVh?= =?utf-8?B?UmQ3Qkh5djFyOFR5Zk1iSzkyUXJjcXhUbXViYmRpcGp6NS9EMVhJbzB3cmU3?= =?utf-8?B?b1JKMlo5dDR3d2N2anYvMnJvMVFxQXBTQVRCSEpPcUxXNFMwUXZ6MmhnZGF5?= =?utf-8?Q?bCYSwRdgKh8sZjhpLLKd8EwIj5PmZs=3D?= X-OriginatorOrg: mq.edu.au --MCBoundary=_12311092247270011 Content-Type: text/plain; charset="utf-8" Content-Transfer-Encoding: quoted-printable Dear All, This thread prompted me to read: JEAN BENABOU (1932=E2=80=932022): The man and the mathematician http://cahierstgdc.com/wp-content/uploads/2022/07/F.-BORCEUX-LXIII-3.pdf which made me think it would be nice to reprint seminal unpublished works of Professor Benabou (such as those discussed in the above) as: Reprints in Theory and Applications of Categories http://www.tac.mta.ca/tac/reprints/index.html simply because Professor Benabou's orginal conceptualization of many category theoretic constructs, beginning with closed to fibered categories, along with, of course, monads/triples (ibid., ref. 12), are worth studying in and of themselves and/or in the context of thier conceptual cousins, so to speak. Here are a couple of illustrations of conceptual kinship that is quite commonplace in science: Professor F. William Lawvere's Axiomatic Cohesion (http://www.tac.mta.ca/tac/volumes/19/3/19-03.pdf) & Professor Johnstone's Punctual Connectedness (http://www.tac.mta.ca/tac/volumes/25/3/25-03.pdf) Grothendieck: Descent (http://www.numdam.org/item/?id=3DSB_1958-1960__5__369_0) & Bastiani and Ehresmann: Sketches (http://www.numdam.org/item/CTGDC_1972__13_2_104_0.pdf) & F. William Lawvere: Functorial Semantics (http://www.tac.mta.ca/tac/reprints/articles/5/tr5.pdf) >From my home turf of neuroscience, the Hebbian learning law: neurons that fire together wire together, which is credited to Donald Hebb (1949; https://drive.google.com/file/d/1_TCefN8KL36RXUA-12S3EZT57SKSoACq/vi= ew?usp=3Dsharing, p. 43) can be traced way back to William James (1890; ibid., p. 2). In closing, in response to my one too many emails on how sets (e.g., {a, b}) that are used to introduce set theory are not exactly Cantor's lauter Einsen (cf. {*, *}), Professor F. William Lawvere, while acknowledging it (spectrum vs. rank; https://conceptualmathematics.wordpress.com/2012/06/08/structure-of-interna= l-diagrams/#comment-17), helped me realize how history is not a home to stay put, but a resource to build on (https://conceptualmathematics.wordpress.com/2012/09/23/comfortable-with-sh= ehes/). Here's one direction to move on i.e., build on Leibniz monad to get to intensive quality (e.g., idempotent; https://cgasa.sbu.ac.ir/article_12425_b4ce2ab0ae3a843f00ff011b054f918b.pdf)= . Thanking you, Yours truly, posina On Thu, Nov 9, 2023 at 12:44=E2=80=AFPM Urs Schreiber wrote: > > Just to note that in 2009 on this same list, the lunch-genesis of "monad"= was attributed to Jean Benabou, see > > Barr 2009 https://ncatlab.org/nlab/show/monad#Barr09 > > Indeed, in print the term was introduced by > > Benabou 1967: "Introduction to Bicategories" (section 5.4) > > together with the astute observation that monads are the lax images of 1 > and thus quite the 2-categorical version of the units=3Dmonads of Euclid. > > https://ncatlab.org/nlab/show/monad+terminology > > > > On Thu, Nov 9, 2023 at 1:22=E2=80=AFAM Michael Barr, Prof. wrote: >> >> People seemed to enjoy my history of the founding of TAC, so I thought y= ou might enjoy my sharing of other historical notes. >> >> This construction was introduced in Godement's book Th=C3=A9orie des fai= sceaux in connection with his resolution of sheaves by "faisceaux mous" (so= ft sheaves) which are an injective class. He called this "la construction s= tandarde". It is not clear whether this was intended to name them or merely= describe them. At any rate, around 1960, >> >> Benno Eckmann and his students took as a name and called them standard c= onstructions. One of the students, Peter Huber, told me that they were havi= ng trouble, in particular cases, verifying the associative law. And then he= noticed that in all the cases he knew, the functor T had the form UF, wher= e F --| U. He wondered if every adjoint pair gave rise to a standard constr= uction and proved that it did. Then another student, Heinrich Kleisli, show= ed that the converse was also true. That gave us the well-known Kleisli con= struction. >> >> In 1963 Samuel Eilenberg and John Moore published a monograph called Fou= ndations of Relative Homological Algebra in which they used this constructi= on as basic. Only they didn't call them standard constructions; they called= them triples. I once asked Sammy why and he replied that it didn't seem li= ke an important concept and it didn't seem worth it to spend a lot of time = worrying about the name. This is in stark contrast with the time he and Hen= ri Cartan spent thinking about the name for their basic sequences. There is= a story, perhaps apocryphal, that their book was in proof stage before the= y settled on the exact name. >> >> So triple was name Jon Beck and I were using in our joint work on homolo= gical algebra. Then in 1966 there was a category meeting in Oberwohlfach an= d there was a lot of discussion of a better name. The next bit of the story= comes out of my extremely fallible memory and could well be mistaken. One = day at lunch I was sitting next to Anders Koch and he asked what I thought = about the name monad. I thought (and still think!) it was a pretty good nam= e and so he proposed it and the assembled crowd agreed and adopted it. I wo= uld have too, but Jon rejected it. Why, I asked him. He did not think it a = good name and refused to use it. He said there was no point in replacing on= e bad name by another. Since we were collaborating and since he was even mo= re stubborn than me, that's they way it was. In our papers, Jon insisted on= putting functions to the right of their arguments, just like reverse Polis= h. >> >> Then we stopped collaborating and, by 1980, I think I was about ready to= start using monad. But then TTT came along and the alliteration was just t= oo good to pass up. Charles Wells agreed on those grounds. >> >> And what about fundamental construction? I spent six and a half months a= t the ETH in Zurich. A few days after I arrived, I got a phone call from Pe= ter Huber, the aforementioned former student of Eckmann's. He had just rece= ived from Math Reviews a paper written by Jean-Marie Maranda that used that= term for the concept and Huber asked me if there was any way to stop that = proliferation of names. As far as I know, that was the only place that term= was ever used. >> >> Michael >> >> >> >> You're receiving this message because you're a member of the Categories = mailing list group from Macquarie University. To take part in this conversa= tion, reply all to this message. >> >> View group files | Leave group | Learn more about Microsoft 365 Groups >> > > > > You're receiving this message because you're a member of the Categories m= ailing list group from Macquarie University. To take part in this conversat= ion, reply all to this message. > > View group files | Leave group | Learn more about Microsoft 365 Groups > You're receiving this message because you're a member of the Categories mai= ling list group from Macquarie University. To take part in this conversatio= n, reply all to this message. View group files | Leave group | = Learn more about Microsoft 365 Groups --MCBoundary=_12311092247270011 Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset=UTF-8 Dear All,

This thread prompted me to read:

JEAN BENABOU (1932=E2=80=932022): The man and the mathematician
http://cahierstgdc.com/wp-content/uploads/2022/07/F.-BO= RCEUX-LXIII-3.pdf

which made me think it would be nice to reprint seminal unpublished
works of Professor Benabou (such as those discussed in the above) as:

Reprints in Theory and Applications of Categories
http://www.tac.mta.ca/tac/reprints/index.html

simply because Professor Benabou's orginal conceptualization of many
category theoretic constructs, beginning with closed to fibered
categories, along with, of course, monads/triples (ibid., ref. 12),
are worth studying in and of themselves and/or in the context of thier
conceptual cousins, so to speak. Here are a couple of illustrations
of conceptual kinship that is quite commonplace in science:

Professor F. William Lawvere's Axiomatic Cohesion
(http://www.tac.mta.ca/tac/volumes/19/3/19-03.pdf) & = Professor
Johnstone's Punctual Connectedness
(http://www.tac.mta.ca/tac/volumes/25/3/25-03.pdf)

Grothendieck: Descent
(http://www.numdam.org/item/?id=3DSB_1958-1960__5__369_0)= & Bastiani and
Ehresmann: Sketches
(http://www.numdam.org/item/CTGDC_1972__13_2_104_0.pdf) &= amp; F. William
Lawvere: Functorial Semantics
(http://www.tac.mta.ca/tac/reprints/articles/5/tr5.pdf)
>From my home turf of neuroscience, the Hebbian learning law: neurons
that fire together wire together, which is credited to Donald Hebb
(1949; https://drive.google.com/file/d/1_TCefN8KL36RXUA-12S3EZT57SKSoACq/view?usp= =3Dsharing,
p. 43) can be traced way back to William James (1890; ibid., p. 2).

In closing, in response to my one too many emails on how sets (e.g.,
{a, b}) that are used to introduce set theory are not exactly Cantor's
lauter Einsen (cf. {*, *}), Professor F. William Lawvere, while
acknowledging it (spectrum vs. rank;
https://conceptualmathematics.wordp= ress.com/2012/06/08/structure-of-internal-diagrams/#comment-17),
helped me realize how history is not a home to stay put, but a
resource to build on
(https://conceptualmathematics.wordp= ress.com/2012/09/23/comfortable-with-shehes/).
Here's one direction to move on i.e., build on Leibniz monad to get to
intensive quality (e.g., idempotent;
https://cgasa.sbu.ac.ir/article_12425_b4ce2ab0ae3a843f0= 0ff011b054f918b.pdf).

Thanking you,
Yours truly,
posina


On Thu, Nov 9, 2023 at 12:44=E2=80=AFPM Urs Schreiber
<urs.schreiber@googlemail.com> wrote:
>
> Just to note that in 2009 on this same list, the lunch-genesis of &quo= t;monad" was attributed to Jean Benabou, see
>
> Barr 2009 https://ncatlab.org/nlab/show/monad#Barr09
>
> Indeed, in print the term was introduced by
>
> Benabou 1967: "Introduction to Bicategories" (section 5.4) >
> together with the astute observation that monads are the lax images of= 1
> and thus quite the 2-categorical version of the units=3Dmonads of Eucl= id.
>
> https://ncatlab.org/nlab/show/monad+terminology
>
>
>
> On Thu, Nov 9, 2023 at 1:22=E2=80=AFAM Michael Barr, Prof. <barr.mi= chael@mcgill.ca> wrote:
>>
>> People seemed to enjoy my history of the founding of TAC, so I tho= ught you might enjoy my sharing of other historical notes.
>>
>> This construction was introduced in Godement's book Th=C3=A9orie d= es faisceaux in connection with his resolution of sheaves by "faisceau= x mous" (soft sheaves) which are an injective class. He called this &q= uot;la construction standarde". It is not clear whether this was intended to name them or merely describe them. At any rate, around 196= 0,
>>
>> Benno Eckmann and his students took as a name and called them stan= dard constructions. One of the students, Peter Huber, told me that they wer= e having trouble, in particular cases, verifying the associative law. And t= hen he noticed that in all the cases he knew, the functor T had the form UF, where F --| U. He wondered if every a= djoint pair gave rise to a standard construction and proved that it did. Th= en another student, Heinrich Kleisli, showed that the converse was also tru= e. That gave us the well-known Kleisli construction.
>>
>> In 1963 Samuel Eilenberg and John Moore published a monograph call= ed Foundations of Relative Homological Algebra in which they used this cons= truction as basic. Only they didn't call them standard constructions; they = called them triples. I once asked Sammy why and he replied that it didn't seem like an important concept and it di= dn't seem worth it to spend a lot of time worrying about the name. This is = in stark contrast with the time he and Henri Cartan spent thinking about th= e name for their basic sequences. There is a story, perhaps apocryphal, that their book was in proof stage b= efore they settled on the exact name.
>>
>> So triple was name Jon Beck and I were using in our joint work on = homological algebra. Then in 1966 there was a category meeting in Oberwohlf= ach and there was a lot of discussion of a better name. The next bit of the= story comes out of my extremely fallible memory and could well be mistaken. One day at lunch I was sitting next to = Anders Koch and he asked what I thought about the name monad. I thought (an= d still think!) it was a pretty good name and so he proposed it and the ass= embled crowd agreed and adopted it. I would have too, but Jon rejected it. Why, I asked him. He did not th= ink it a good name and refused to use it. He said there was no point in rep= lacing one bad name by another. Since we were collaborating and since he wa= s even more stubborn than me, that's they way it was. In our papers, Jon insisted on putting functions to the r= ight of their arguments, just like reverse Polish.
>>
>> Then we stopped collaborating and, by 1980, I think I was about re= ady to start using monad. But then TTT came along and the alliteration was = just too good to pass up. Charles Wells agreed on those grounds.
>>
>> And what about fundamental construction? I spent six and a half mo= nths at the ETH in Zurich. A few days after I arrived, I got a phone call f= rom Peter Huber, the aforementioned former student of Eckmann's. He had jus= t received from Math Reviews a paper written by Jean-Marie Maranda that used that term for the concept and Huber asked = me if there was any way to stop that proliferation of names. As far as I kn= ow, that was the only place that term was ever used.
>>
>> Michael
>>
>>
>>
>> You're receiving this message because you're a member of the Categ= ories mailing list group from Macquarie University. To take part in this co= nversation, reply all to this message.
>>
>> View group files | Leave group | Learn more about Microsoft 365 Gr= oups
>>
>
>
>
> You're receiving this message because you're a member of the Categorie= s mailing list group from Macquarie University. To take part in this conver= sation, reply all to this message.
>
> View group files | Leave group | Learn more about Microsoft 365 Groups=
>
 
 
You're receiving this message because you're a member of the Categories mai= ling list group from Macquarie University. To take part in this conversatio= n, reply all to this message.
 
View group files   |   Leav= e group   |&n= bsp;  Learn more about Microsoft 365 Groups
 
--MCBoundary=_12311092247270011--