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=DKIMWL_WL_HIGH,DKIM_SIGNED, DKIM_VALID,HTML_MESSAGE,MISSING_HEADERS,RCVD_IN_DNSWL_NONE, T_SCC_BODY_TEXT_LINE autolearn=no autolearn_force=no version=3.4.4 Received: (qmail 23743 invoked from network); 13 Nov 2023 22:16:24 -0000 Received: from mail-sy4aus01hn2244.outbound.protection.outlook.com (HELO AUS01-SY4-obe.outbound.protection.outlook.com) (52.100.199.244) by inbox.vuxu.org with ESMTPUTF8; 13 Nov 2023 22:16:24 -0000 ARC-Seal: i=4; a=rsa-sha256; s=arcselector9901; d=microsoft.com; cv=pass; b=NKt+tCNv3lZI9Rxu2VjS2MZRXVodD469+PznZgsKdtoti2qcJR7jAZcYqhdLs3HI8Pc7/ob7sFCpVzOolXFt6GPOs4+W2L4LgiXBx8KgAKdEWyFZ96Hfx0Nk8ZjCnOWjFvz0PuBC4yAz4hnguZPWRUYI7yzJ3t3kHYUoEyVY0X65nu3RsHrLAW1GRKxMxL88UWwHfhxRp9GoJSSZwJDMvMYH/D0cRDOY1QOwB3fo4o0IIsGe2xPw/+DFr1M8m3DkWqE49IT01o1s4HgbZ/t8GxSAoeHA4bl4RLgdd4+QKU1psI8sdTabrV6V5PvkwaxxcHUBE0NIHNm1m8KpsF9hVQ== 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=oSfm/6NYmrwHEY8K8/Wh/14PWU0z+yNSuQI611S9jC8=; b=SsdSOWM4vKganTaFs3OLs0RFKP3Atnv6uzxx3QGcZTobMPSV4uVz+7HGYtjPSSgyS9lG0UtRt6XoFjscVfh1ScOy9KDhzDm+RkmgW6svWW8dZK7XYhwe/8PHqkVS5HPPslxWUe5e/Gt9xmzTepRGSS+g/cYHVPnn9sKci5yFvHTzi7W/rsEjL49zg8u0HhcqvQRsjxvl/ite5zx/sgTvuS/8/kbDlj2WDXFV0GC+lOwyVQq08LdtVMvcfLu+pztc+aBDZKDz8336CjEcP2G42LOpAO7dNqo1/AKyCEaaJRRqD17NG13AjemEILpb/zSSNKJg+yI6NsJUY5YP3B93Jw== ARC-Authentication-Results: i=4; mx.microsoft.com 1; spf=pass (sender ip is 138.23.62.71) smtp.rcpttodomain=mq.edu.au smtp.mailfrom=ucr.edu; dmarc=pass (p=none sp=none pct=100) action=none header.from=ucr.edu; dkim=fail (signature did not verify) header.d=ucr.edu; dkim=fail (body hash did not verify) header.d=ucr.edu; 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=oSfm/6NYmrwHEY8K8/Wh/14PWU0z+yNSuQI611S9jC8=; b=X3+bl7jGG4caCRkSRkJc5fBczpM6zKTUrUxOMtiYvFxZpwWUkxF+waIQgHLQgo6Ap5+d9sgfNf8lYEhxwE/BXwb1pswe5hI7sg3Sp9YubG2NrQCCzZYHstVlejwl630BF7LuUzIFQTz2dT5SVcJ/iFehVYeMp0bk2DNiE3dWxGmiJFStiW0mnuBUqlmlzWA0g+4GesuWpwxhi+MWt4AJP5NT5HhFVG/efwErb6Ahvwnh4bR7MBdPWbmy4yaHjzzufVI9njNl7WutWnld2eoSmqcf+TObw8CHcPBIfvlfKLV1upIK/MN5Mfk77ZgICsRVB2yQXVaetSb4aIpBux60vg== Received: from SmtpServer.Submit by SY7PR01MB8160 with Microsoft SMTP Server id 15.20.6977.31; Mon, 13 Nov 2023 22:16:20 +0000 ARC-Seal: i=3; a=rsa-sha256; s=arcselector9901; d=microsoft.com; cv=pass; b=Rcs3VLm+x391w6YlJ7dhSAi5mPFsqmE2LBtoL/iEe6l1NfAnS3PF+FDsxbukC0sZt4WBcGEVp5pKh+YARCBFNmij0LXUh7mIBcthfLDmDGQnVGEj6gCo/Ru7Ekp0WjXyzOCZPDERWLV7RRgSCAV5KLAeu6QUP4WI2jNvi18tfQ/zjXaF4uEKV4QAkj9pvGL8UEz/7AzHyIizQqW56c6RLZ4guQxYemwCGqZ/yIXx2a3/7KMnN5F+zDFvpy1so1kFBr2DAdf2ZVKdmero52ztsOJugjLbKJAllxy9XvMf6bEryPbxd/KKsq0wQh/YgOgE+mjNg5GQQO5NuK/IRYon+w== 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=pos6F+ti68p7+qU1WN+J4DXnKDq8WedTBpiUSvuKbQs=; b=NM0bqg7muewNe8C0i7oeaYGRonxwiYiA7txTM//qh3Fl1m027YzPU0PD8GqqRITmeNRE/iOlrGQ4XRNZwnzEZ1k+S4RRn6b+oAOTfz4Fp98domNH9jIfWM9KurNZoD6LBjgIRU1uva4+2wFsj/eT8JeLJyR7jOp8TlnDRzg6lW6HAPmnnaHxLqg2qDYs2+4Ms0Ir7dzprcG+Vp0LwOrRUd7P6Cpx/0mFFiNq6NPI7yQJlJnHYW9Y+gpeiKzVYKrGCZ6cJNz1Wx3S/JWIi1fJnMhiHrv7ceNk2FxITeTe5U25npiQ/7RAww7mVK9e/QxM8Wun//N0zpuuKrxUoIKBGg== ARC-Authentication-Results: i=3; mx.microsoft.com 1; spf=pass (sender ip is 138.23.62.71) smtp.rcpttodomain=mq.edu.au smtp.mailfrom=ucr.edu; dmarc=pass (p=none sp=none pct=100) action=none header.from=ucr.edu; dkim=fail (signature did not verify) header.d=ucr.edu; dkim=fail (body hash did not verify) header.d=ucr.edu; arc=pass (0 oda=0 ltdi=0 93) Received: from SY0PR01MB9083.ausprd01.prod.outlook.com (2603:10c6:10:21f::10) by SY7PR01MB8160.ausprd01.prod.outlook.com (2603:10c6:10:1e7::7) with Microsoft SMTP Server (version=TLS1_2, cipher=TLS_ECDHE_RSA_WITH_AES_256_GCM_SHA384) id 15.20.6977.31; Mon, 13 Nov 2023 22:16:14 +0000 Received: from SY4PR01MB8050.ausprd01.prod.outlook.com (2603:10c6:10:1c1::14) by SY0PR01MB9083.ausprd01.prod.outlook.com (2603:10c6:10:21f::10) with Microsoft SMTP Server (version=TLS1_2, cipher=TLS_ECDHE_RSA_WITH_AES_256_GCM_SHA384) id 15.20.6977.31; Mon, 13 Nov 2023 22:16:11 +0000 Received: from SY4PR01MB8050.ausprd01.prod.outlook.com ([fe80::64cf:b0eb:a004:dfec]) by SY4PR01MB8050.ausprd01.prod.outlook.com ([fe80::64cf:b0eb:a004:dfec%3]) with mapi id 15.20.6977.029; Mon, 13 Nov 2023 22:16:10 +0000 ARC-Seal: i=2; a=rsa-sha256; s=arcselector9901; d=microsoft.com; cv=pass; b=YaVswaHMLs8RBxdE1rbcWzN3OJWysC9kWAlZXKtCYl50IDfkWBOwvP4YNy7Dgn3cZwlZ4LEXTf0UZY9PtlRmh9rQDUEvGj77h50tjN3iUcvdw439xwvoXXsPYpSZ/J8e6gFBWsqSb9CdYavZDUIYya2DXtYUAflBcV809WdTmJY40wtnGhQ6to02vo5DUnMsfoVwJd6I6GfAmueyNi6MnE0rpazwKgyuQ96rPLB+UBY6ja3l5L57D5WLPwnoY4VqNOmUgRCZoT7Yi4PHqB5wQYdOZA9T384camPJ8yxXBpHzvS6y5O3mCYOb/XITaFJfmnGXoyK1rzyxLewGu9KuQQ== 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=pos6F+ti68p7+qU1WN+J4DXnKDq8WedTBpiUSvuKbQs=; b=T2k7AerExFRhATHTHgapwZvQ1PkwNnF6pz0FtRDefwelALjhUgl4oHvaGAVnTKtwCh+VCm9LQUFxU5NhVS1BY7BPsnnxrLxD5sF9+jQQFs90DMKLXCR6V/vO4VFl0igjhHF7X0OezbnylaTMu0xJrg7L2aT42EYyaVef2z/LXbgjWMGDJY+3z7rPz5z/RYanAnhtxcKQrNtWboDDY2tAPAi2fDdFHxxXUI/qiOcyTD+vpBcunEOMgm2tRzxrFcLQ1FZntyHCtMw/jga0wzk5hin/cHhCrnJhQNaR5P24oAkYGB+lv11AkTcW4VY5my3JBU6IDi47oqyHnarVm4zVRA== ARC-Authentication-Results: i=2; mx.microsoft.com 1; spf=pass (sender ip is 138.23.62.71) smtp.rcpttodomain=mq.edu.au smtp.mailfrom=ucr.edu; dmarc=pass (p=none sp=none pct=100) action=none header.from=ucr.edu; dkim=fail (signature did not verify) header.d=ucr.edu; dkim=fail (body hash did not verify) header.d=ucr.edu; arc=pass (0 oda=0 ltdi=0 93) Received: from SY5P300CA0047.AUSP300.PROD.OUTLOOK.COM (2603:10c6:10:1fe::14) by SYBPR01MB6272.ausprd01.prod.outlook.com (2603:10c6:10:106::10) with Microsoft SMTP Server (version=TLS1_2, cipher=TLS_ECDHE_RSA_WITH_AES_256_GCM_SHA384) id 15.20.6977.31; Mon, 13 Nov 2023 22:15:40 +0000 Received: from SY4AUS01FT019.eop-AUS01.prod.protection.outlook.com (2603:10c6:10:1fe:cafe::a8) by SY5P300CA0047.outlook.office365.com (2603:10c6:10:1fe::14) with Microsoft SMTP Server (version=TLS1_2, cipher=TLS_ECDHE_RSA_WITH_AES_256_GCM_SHA384) id 15.20.6977.29 via Frontend Transport; Mon, 13 Nov 2023 22:15:40 +0000 Authentication-Results: spf=pass (sender IP is 138.23.62.71) smtp.mailfrom=ucr.edu; dkim=fail (signature did not verify) header.d=ucr.edu;dmarc=pass action=none header.from=ucr.edu; Received-SPF: Pass (protection.outlook.com: domain of ucr.edu designates 138.23.62.71 as permitted sender) receiver=protection.outlook.com; client-ip=138.23.62.71; helo=mx6.ucr.edu; pr=C Received: from au-smtp-inbound-delivery-1.mimecast.com (103.13.69.22) by SY4AUS01FT019.mail.protection.outlook.com (10.114.156.121) with Microsoft SMTP Server (version=TLS1_2, cipher=TLS_ECDHE_RSA_WITH_AES_256_GCM_SHA384) id 15.20.7002.14 via Frontend Transport; Mon, 13 Nov 2023 22:15:39 +0000 ARC-Message-Signature: i=1; a=rsa-sha256; c=relaxed/relaxed; d=dkim.mimecast.com; s=201903; t=1699913739; h=from:from:reply-to:reply-to:subject:subject:date:date: message-id:message-id:to:cc:cc:mime-version:mime-version: content-type:content-type:in-reply-to:in-reply-to: references:references:dkim-signature; bh=pos6F+ti68p7+qU1WN+J4DXnKDq8WedTBpiUSvuKbQs=; b=IJQXlzkj6XzgtM7EGdrQclIebxaagEh1grzYYJ0VdzkLSeBJ8AxnNWxpuzLorbdHoqjjnr mMc0ML1PSt7N2mOcDEkNhYmdRTJCg7SeyyPY7Y77Yl2RUY+3UGWB051DtDtccXX2CDhpqt ykjLTjb3oVpggHzIF+sOtdCpiSim+YYMW4xpUZ/k1eSXkMtM21Ca66pu+RTqUgzPlNjAJ7 PRqhDkJzex1DYWesqoZpoinhcGYOtcmPXjeT4lgq8J3mbVy17GDn8rxQdX/IjyTnYfR9DU K8vMlvB+sb3T5wDKgikIryRmH7VsXk8t2NJZRSndKZQUEqd0H8qlXx6loLv91Q== ARC-Seal: i=1; s=201903; d=dkim.mimecast.com; t=1699913739; a=rsa-sha256; cv=none; b=fANVx0maiBninZktHE5cmyr3jEdjIVH83zmd4Szgxnyu/7O8fQxNORLP+31pEa7O4w5t4B hcNSB+9LUoN01/wWTVi65jpVLhQefMurNNUnslvOO5dPThpKrF8B08zZWCXH9/peEhC1pX HD0NuVEWXfh/HvOZhle38Hda82QhDCuXZmVBbqxDwlwgS5o8PxfrBBM/bCvB1SRjJ0mSPP MrmeON8KKFVaEHZc1c8HOavD4bE1QSjLzdmenVFM6roOX4aP7zv/JdJlc+Zj4qkRybiCmv 5oJJByBzdneJosFufhFryXoPRvnWZpOb65HAPi47kvEwEARmP4lO1bh6QOtHNw== ARC-Authentication-Results: i=1; relay.mimecast.com; dkim=pass header.d=ucr.edu header.s=selector3 header.b=FfmUtynG; dkim=pass header.d=ucr.edu header.s=rmail header.b=Ya5lF5Lf; dmarc=pass (policy=none) header.from=ucr.edu; spf=pass (relay.mimecast.com: domain of johnb@ucr.edu designates 138.23.62.71 as permitted sender) smtp.mailfrom=johnb@ucr.edu Received: from mx6.ucr.edu (mx6.ucr.edu [138.23.62.71]) by relay.mimecast.com with ESMTP with STARTTLS (version=TLSv1.2, cipher=TLS_ECDHE_RSA_WITH_AES_256_GCM_SHA384) id au-mta-57-FDUEQlfbMUSyyb6cxo8M-Q-1; Tue, 14 Nov 2023 09:15:36 +1100 X-MC-Unique: FDUEQlfbMUSyyb6cxo8M-Q-1 DKIM-Signature: v=1; a=rsa-sha256; c=simple/simple; d=ucr.edu; i=@ucr.edu; q=dns/txt; s=selector3; t=1699913738; x=1731449738; h=mime-version:references:in-reply-to:reply-to:from:date: message-id:subject:cc; bh=cBRRkBNW9aGAuwVHJzfHn1iSGehvHAUgWIHXRLDYjLQ=; b=FfmUtynGmhu/Eq/dDwHzmRqwL7y+JB/gkWrBer1uC8Jmp89hwKnUFuYi X5CGW7aVmHAEhM1k7xgry1q5G5xIRmkvLgWzIXLo8h4EIfVjr0LcQo1ho 6I+/x7tLSmjjo2lbImkPr+yk7LL1gFB8IDcjdkoRSM4iS0/fIyZ1mekX+ ag+HBtA49w55j3Ie8O/yoj86kXfCZgiJSW7M+UjzaczXhFUk8L13RcBZJ G/u3CSM3IkQ+ZNzLlwFL7QaVFzHKypmt2PfTQ4Ndb6N4xEXlv37wHgfAO caD+ND3JsIVcDKxFcKm1y++iQBoBHilOjV6meVkz4e+CyNf+4bfeUePEy g== X-CSE-ConnectionGUID: alT6zC5ZTZyj+6h+QOMCog== X-CSE-MsgGUID: TxeOzV/BRTGj98YeuNNJEA== Received: from mail-pg1-f199.google.com ([209.85.215.199]) by smtpmx6.ucr.edu with ESMTP/TLS/ECDHE-RSA-AES128-GCM-SHA256; 13 Nov 2023 14:14:32 -0800 Received: by mail-pg1-f199.google.com with SMTP id 41be03b00d2f7-5aaae6f46e1so5800848a12.3 for ; Mon, 13 Nov 2023 14:14:31 -0800 (PST) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=ucr.edu; s=rmail; t=1699913670; x=1700518470; darn=mq.edu.au; h=cc:subject:message-id:date:from:reply-to:in-reply-to:references :mime-version:from:to:cc:subject:date:message-id:reply-to; bh=8mFvSOPvFaryTwLXuLS59PsURmRy8FaFaTeLYZE7PxY=; b=Ya5lF5LfgMR317qDbZDIcmf+kQ7GiucPjFHuJxencxqea09nWvUgxTc1Zj2C2nNNO/ 6Lk1QEC++/mxAyDox1zih98P/MAslizKJUbb1mypEPehJ5yoD7c2rS573G4sZmbfiQEc Eg1/OhQ2zvwH97ksyoD5wQPQIaKtlkWOwLu4U= X-Google-DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=1e100.net; s=20230601; t=1699913670; x=1700518470; h=cc:subject:message-id:date:from:reply-to:in-reply-to:references :mime-version:x-gm-message-state:from:to:cc:subject:date:message-id :reply-to; bh=8mFvSOPvFaryTwLXuLS59PsURmRy8FaFaTeLYZE7PxY=; b=O9V8Gltmf7Qp4isNzz/Yll8rkW7q6VBJ4PnL+5Xz2MUrT4Bv+Hw+zr9qxr/C3uoWkV e1xOI/v3tVr7//ExvwLHxO3E/IYkf2JTb8+QAH/ZoR8JezXO2w9W/rbx++STvhN8iFtC JXB8m+6Kmofo9Opz8dG3IaoPJHrFU5XpsEGQLahhifbJKWVU3OD53e0uSyyzS4MMAWpC lTHfDwpWhObKi1FrkSVxzouaItjTkTCWFZRY5IJHr4CXOl9uMpOasRzIzSRmPYGBFcup HaIKS6laT97sP1MI0ktOhpD4MfkgMH4o3psuixWJm5IQDyoWDn6a3zEnrwkZ7oxfwR1G iTjQ== X-Gm-Message-State: AOJu0YzySPm6+OgP92yW5ToEZYW1+z+wFRbjZP/hRUqxSWW5ksJH1I7W 7D0qIjjctCE7q0n3oCU3WkJJJPgsg3ylKdUi2GvSTvjzsXtnI27H9dda4zWIxkje9DHu+i6q+dy PQaDauaknF/4vxeDdFdO9u/itaMl5VueH6HzIYpbdLQ== X-Received: by 2002:a05:6a20:1585:b0:15e:a653:fed5 with SMTP id h5-20020a056a20158500b0015ea653fed5mr10156155pzj.16.1699913670674; Mon, 13 Nov 2023 14:14:30 -0800 (PST) X-Google-Smtp-Source: AGHT+IFjD+rYefz5Ae7+bNFex5PqwO34y6CU26qsN3/OV7bQYUkCWIcNI5ICIXUCz6IbpJmLtC2k3UBFPJpZh06+kmk= X-Received: by 2002:a05:6a20:1585:b0:15e:a653:fed5 with SMTP id h5-20020a056a20158500b0015ea653fed5mr10156137pzj.16.1699913670373; Mon, 13 Nov 2023 14:14:30 -0800 (PST) MIME-Version: 1.0 References: <2078BAE5-12A8-4871-8DCE-C4B1B8285B02@mq.edu.au> <18B15895-9B03-4B49-9D0E-8448D0FAB283@mq.edu.au> In-Reply-To: <18B15895-9B03-4B49-9D0E-8448D0FAB283@mq.edu.au> Reply-To: baez@math.ucr.edu From: John Baez Date: Mon, 13 Nov 2023 22:14:18 +0000 Message-ID: Subject: Re: The game of the name: Standard constructions, triples, monads, fundamental constructions CC: Categories mailing list Authentication-Results-Original: relay.mimecast.com; dkim=pass header.d=ucr.edu header.s=selector3 header.b=FfmUtynG; dkim=pass header.d=ucr.edu header.s=rmail header.b=Ya5lF5Lf; dmarc=pass (policy=none) header.from=ucr.edu; spf=pass (relay.mimecast.com: domain of johnb@ucr.edu designates 138.23.62.71 as permitted sender) smtp.mailfrom=johnb@ucr.edu X-Mimecast-Spam-Score: 2 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=false;Mimecast Threat Dictionary=false;Custom Threat Dictionary=false Content-Type: multipart/alternative; boundary="00000000000078c640060a0ffe84" Return-Path: <> X-EOPAttributedMessage: 0 X-EOPTenantAttributedMessage: 82c514c1-a717-4087-be06-d40d2070ad52:0 X-MS-Exchange-SkipListedInternetSender: ip=[138.23.62.71];domain=mx6.ucr.edu X-MS-Exchange-ExternalOriginalInternetSender: ip=[138.23.62.71];domain=mx6.ucr.edu X-MS-PublicTrafficType: Email X-MS-TrafficTypeDiagnostic: SY4AUS01FT019:EE_|SYBPR01MB6272:EE_|SY0PR01MB9083:EE_|SY7PR01MB8160:EE_ X-MS-Office365-Filtering-Correlation-Id: 17b6092f-b9ce-4c43-9a91-08dbe4961193 X-Moderation-Data: 11/13/2023 10:16:09 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: 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 X-Forefront-Antispam-Report: CIP:103.13.69.22;CTRY:US;LANG:en;SCL:1;SRV:;IPV:NLI;SFV:NSPM;H:mx6.ucr.edu;PTR:mx6.ucr.edu;CAT:NONE;SFS:(13230031)(4636009)(39860400002)(136003)(396003)(346002)(376002)(451199024)(82310400011)(64100799003)(8000799017)(109986022)(48200799006)(61400799009)(40470700004)(75432002)(83380400001)(40460700003)(26005)(336012)(156005)(32850700003)(41300700001)(7596003)(2906002)(55446002)(82740400003)(32650700002)(66574015)(35950700001)(8936002)(4326008)(8676002)(6666004)(33964004)(786003)(316002)(68406010)(42186006)(70586007)(88732003)(89122003)(498600001)(76576003)(7406005)(7336002)(7366002)(41110700001)(7416002)(9686003)(40480700001)(7276002)(5660300002)(44832011)(41080700001)(41090700016);DIR:OUT;SFP:1501; X-Auto-Response-Suppress: DR, RN, NRN, OOF, AutoReply X-MS-Exchange-CrossTenant-Network-Message-Id: 17b6092f-b9ce-4c43-9a91-08dbe4961193 X-MS-Exchange-CrossTenant-Id: 82c514c1-a717-4087-be06-d40d2070ad52 X-MS-Exchange-CrossTenant-AuthSource: SY4AUS01FT019.eop-AUS01.prod.protection.outlook.com X-MS-Exchange-CrossTenant-AuthAs: Anonymous X-MS-Exchange-CrossTenant-FromEntityHeader: Internet X-MS-Exchange-CrossTenant-OriginalArrivalTime: 13 Nov 2023 22:16:10.9821 (UTC) X-MS-Exchange-CrossTenant-MailboxType: HOSTED X-MS-Exchange-CrossTenant-UserPrincipalName: dT7I90KXGiJcbvbAYR3eiFJ8St8K7Mo5rgj2BbZJKHiVewK/AHf2cSN5VSXK8j7Lmoc0N9iukIYy7TvBaWpFO/mXac4WwKndhCbsuj/5z+462gurO+boYN58qs/bMqUqeY3wMLNfvCWdI+8uY6UAtiFwg41h4/N/uiqIpWceLWERQWL5RydD+6JKYY1/eByp X-MS-Exchange-Transport-CrossTenantHeadersStamped: SY7PR01MB8160 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?Qi9aRjAwMml2S2tqaUtvb3BzeG9DNDI1K0QrdmNBdzhVY2JydldrNGlGeFJz?= =?utf-8?B?SzE4emFObDdPQ25lQ2xGdGtHZUVjakJzNjRXeHFobDJ6SVY3Umg0ek5uNCtF?= =?utf-8?B?bWFiZnM3SFFuVlpycTUyaDRVc2JDbGJ4bVhsdVNiWW1DcktLN1VqZmpTS0U3?= =?utf-8?B?b1ZtcTVPZmVWcmRtRFNyV0ptbjZoR0pWNnZVR2hVcHNhTnppQWNtdW1hdGJX?= =?utf-8?B?VHJSd2xSekhLcFJNNEYzRWJNWFY3TldibldSdGUzRktHajhmWVVOd2ZEVWVJ?= =?utf-8?B?VURmNkR6b2hwN0I1d1k5cWZoQmhkbUg4NkFwaklvbmd0UDdZTlVFZXg1VjBT?= =?utf-8?B?Vk1qSjVRUXZtRlR0ZzZBQi9tb3NRVG8wYlBNcEhKTVE3QlpNQkE4Mk40MFhn?= =?utf-8?B?ZlhjOWRsdnlBTWNiVm9yaE9PQVZCQTRMRUp5YW5oUk54OVpFVDY2djYrcmNn?= =?utf-8?B?eW1RZzNRTXpLcnJoeEhjOURrTW9yaDNUYjlHVTdtMUh2elhiQW5qRlVKRzFW?= =?utf-8?B?dXhMa0lnQS9LcndrRzR2YmhoQXdQU21oQWpOeVRETW5PT05vT1hSejJwa0hh?= =?utf-8?B?MEs0NGlEWE41SWFhaEptVjBuK1pQdnBUamlUTVBMMVJwWGJ5dmpEWjVPYmRr?= =?utf-8?B?UTgySUhGMFBPOWVvZU5FVnlvOERsRXhraVhiclBETDZVS1MremJJSUJBa3lw?= =?utf-8?B?QmcrZlBlRXEvOEx1dW1CVUVkT01wOWFpa2lqQThtaDRRQlVpMGd6UzVFaUJl?= =?utf-8?B?Q3VtcGhKTEJJS3dBWGJrLzIyWGlncDlnNFozWlVHQnVVTEg4MDRHTTk4T0dZ?= =?utf-8?B?Ti9zditQYnlkVnhRTVYrc3VLKzNqYmhOZlJsSWZSd0pWV0RCNjNrSi96Vjht?= =?utf-8?B?WndNRW1ZM0ZoQjloM0t3V1lLTVBsc3JnSExEc0Z5R25jRlRUWXFkTGx6eFQw?= =?utf-8?B?bkNpUE8vSXFUTzVQMEFMdExlaEt5NU83SzFkT25mOUJiNGxuVyt1ZHlhTStY?= =?utf-8?B?cFVFREY0b3RoaWY1OFBFSWNaV3NNTUpXeUVCOFBlYy93YzhGejFRZ2RjOE5o?= =?utf-8?B?N1R2ZHFrR2VlT010NVNDTkpETTcxVmhmd0hUT0FZVGgwdEd1bHhNcVFiQmVt?= =?utf-8?B?ZmFIc2I4ekw3aDdNci9La3Q2OU1PZktxWDI4RTEweVFLemlmVzZCaTB0Nk9i?= =?utf-8?B?MDVWZXYrZFNNbjQyU0V6Z3pwYTVlZkkzS3lYVnV4SzFyaWd6K0JGTUhHQzdW?= =?utf-8?B?TjlCQXFjanhzUGFHUVg4QnFMdWZGcG1qVmVZSTBZUGt2aGs2RVBHTFQrM3hj?= =?utf-8?B?bjV2ODRhTitzc3ZKT1o1UDFsb1pLRWFjMlc4ZXlKeXgrNnNRRldKNFJDRTlF?= =?utf-8?B?U0N1NjZ6RmVhckpzTW5BbFB1WHlVN2RJZ2x3UmpRYlhHT0s3cmhtNTh1UHkz?= =?utf-8?B?WCt3S2gxWWI0QUdBcWs4dGk0RXF6WU1aWnB2MWhUZ2t2elU5Vkkrd3VGOTNM?= =?utf-8?B?c2V6UHIycEVZdUVTREllSEpJZXBDK2NTUDRFWFhZODlLaU9QL010N2UzTzQ3?= =?utf-8?B?UUptcGdYTHliRW9RbkhnN0RxeUozYzY3K1JXNDlobE5ObFd1ZXl6andBaFJE?= =?utf-8?B?UEJtQWh0TGM2REN1aHhEMnFta3dPd1dBdXg3cjhtcG15R2JWTVYvR01uU1h2?= =?utf-8?Q?i5BXCXxUCj2y7a/aYbtX?= X-OriginatorOrg: mq.edu.au --00000000000078c640060a0ffe84 Content-Type: text/plain; charset="utf-8" Content-Transfer-Encoding: quoted-printable Hi - It is not very important, but I was amused to discover recently that Mac La= ne's famous 1963 paper on monoidal categories, "Natural associativity and c= ommutativity," does not mention "monoidal categories". Instead he called = them "bicategories"! Later in this paper he writes "Bicategories have been introduced independently by several authors. They = are in B=C3=A9nabou [1], with a different but equivalent definition of "coh= erence," but without any finite list of conditions sufficient for the coher= ence." This is not B=C3=A9nabou's famous paper on bicategories: instead it's "Cat= =C3=A9gories avec multiplication", where B=C3=A9nabou introduces a prelimin= ary concept of monoidal category, which he called "cat=C3=A9gorie avec mult= iplication". Furthermore, it's now recognized that B=C3=A9nabou's formulation of coheren= ce for monoidal categories is not quite right. Benabou's version is along = the lines of "all diagrams formed by associators and unitors commute", and = he does not state this in a way that rules out problematic cases caused by = coincidental equations between objects. It seems the history of mathematics is endlessly tricky. Best, John Baez 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 --00000000000078c640060a0ffe84 Content-Type: text/html; charset=UTF-8 Content-Transfer-Encoding: quoted-printable
Hi -

It is not very important, but I was amused to discover recently that M= ac Lane's famous 1963 paper on monoidal categories, "Natural associati= vity and commutativity," does not mention "monoidal categories&qu= ot;.   Instead he called them "bicategories"! &nbs= p;

Later in this paper he writes

"Bicategories have been introduced independently by several autho= rs.  They are in B=C3=A9nabou [1], with a different but equivalent def= inition of "coherence," but without any finite list of conditions= sufficient for the coherence."

This is not B=C3=A9nabou's famous paper on bicategories: instead it's = "Cat=C3=A9gories avec multiplication", where B=C3=A9nabou introdu= ces a preliminary concept of monoidal category, which he called "cat= =C3=A9gorie avec multiplication".  

Furthermore, it's now recognized that B=C3=A9nabou's formulation of co= herence for monoidal categories is not quite right.  Benabou's version= is along the lines of "all diagrams formed by associators and unitors= commute", and he does not state this in a way that rules out problematic cases caused by coincidental equations between = objects.

It seems the history of mathematics is endlessly tricky.

Best,
John Baez


 
 
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
 
--00000000000078c640060a0ffe84--