From mboxrd@z Thu Jan 1 00:00:00 1970 Return-Path: <> X-Spam-Checker-Version: SpamAssassin 3.4.4 (2020-01-24) on inbox.vuxu.org X-Spam-Level: X-Spam-Status: No, score=-2.1 required=5.0 tests=DKIMWL_WL_HIGH,DKIM_SIGNED, DKIM_VALID,HTML_MESSAGE,RCVD_IN_DNSWL_NONE,T_SCC_BODY_TEXT_LINE autolearn=ham autolearn_force=no version=3.4.4 Received: from AUS01-SY4-obe.outbound.protection.outlook.com (mail-sy4aus01hn2201.outbound.protection.outlook.com [52.100.199.201]) by inbox.vuxu.org (Postfix) with ESMTP id 7879A2B9D1 for ; Mon, 5 Feb 2024 01:49:02 +0100 (CET) ARC-Seal: i=5; a=rsa-sha256; s=arcselector9901; d=microsoft.com; cv=pass; b=mmVpQNSOOsTf6Zu+Azkg5+Ok7ZbpGbCQf+09Yu2J/KA6gyVr4pV5+uaWGm/VWYzq0FcYWlqo+hJ8HZB7457008Po0y9t9DQgpVNgY54/xhMy4jEu6UOsqgArucmFziXKT4YwLsDJOUHsf1TcmaTJZ+Q+Bq9biNf52IErnmBinAFXgA783PXqXfFv1GALt6cQ4uescbU3j3jnEM2EWCZAOWR6iYckHmQLyvNH9/M397XLlPTTY9QCUjVlj+xtMjOLDjT2eTcdpLyvtqVCpSXVqXeGh0HyFIZXrYb7mGgKvgFK2hT4D5oFlAUoMcpmhLquLkfhzWcfjDPEqOPz533BBg== ARC-Message-Signature: i=5; 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=nwk7d7LKo7sMHMerZSBF97UaZGqpjPvkqcz0UDXh5QY=; b=ip5ruxzycf2yuCwzbHW5BJmdqckt2VkXV0aVZECyUX4IrMASEeZT/BmRxMuGdOSzipet3Vv5YUaAnoC2qo44hBzbwod5wFp2hPxyDKG9SkJvbtOFqJMMCwFcdT49lmElV1DwlKYLwayI4HzWdw+5Qw4V/CVia9geIGtr6u+uQOs/PvgmC4935WB8EpoQeINbTjijmkMscDw/nTioWBGDUrsadnQoCdONF/pgmqcojk7wD+V+wve/VBsf3eijx1Wpa9lTcFN0TXqHm7W1c6XkAiFJhPoX9yZcHflQ/kVhlJhVp9qrf5Z6q0zVN2ZPTLp/TM20m0BjM7ujVGuKYgkrsg== ARC-Authentication-Results: i=5; mx.microsoft.com 1; spf=pass (sender ip is 52.101.56.11) smtp.rcpttodomain=mq.edu.au smtp.mailfrom=ksu.edu; dmarc=bestguesspass action=none header.from=ksu.edu; dkim=fail (body hash did not verify) header.d=ksu.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=nwk7d7LKo7sMHMerZSBF97UaZGqpjPvkqcz0UDXh5QY=; b=QiDl9MIGM6tFdQS1VIeMRKl4bMfcYKHZOgSrTUQa/xbPxdNSUsI+q/GLGC+eSKvgByZz6ml/LRVkNr29A6Kg5qldEKA0BkHwP9fX3yPheiABaGFoL6Epsy/Aimo3wPxAntzyZIe1FXSNfWh14/MoF8O+Po4XJhy3WFOcAKz6l/z10o72NIExEoQXkY4QEgF2Ul4TIW+dTS9FrTaZDJmSy6650Lv+e7XlGOHkBK4JvyQdr1jpezSQzQ+OPe2Y5x4GM2H6vsPx4aE0lHvoEHNPGAk2DSqpBw54tNyM2i689wBqnHBPW+92hIIhE/h0phMamj4voPTmlG8ynuLBUpU1Qg== Received: from SmtpServer.Submit by SYBPR01MB5757 with Microsoft SMTP Server id 15.20.7249.34; Mon, 5 Feb 2024 00:48:59 +0000 ARC-Seal: i=4; a=rsa-sha256; s=arcselector9901; d=microsoft.com; cv=pass; b=ZHdBCe0Y68d4zVfDtFh0DzxY7yqhDO3/5qVxbyK9T9HovLM5tSzZHJ4pDuC0vzImj/g977E4jIKKHJuX2GSIG6hwirAD7EiVdOBYWWvAmpwIAD4TpWxZt/5qOO58YTmEk0JxCQn/LBeX6f2ibeNB2e++bSjZYdO5gkhxVgJUC4qTqp9uEWeGje4ftN0QLzgQzVpbtY2bRslZRP9ai4ie3HPkQ01y5AuOWdkHCtgEFRQV2FOQt4QGmDO3yafoO4+rLKqySYAvpjG34bBr/C3048NXcEz9ModgrhxELJgNuXXdEuc5a7d4tsG3VzKyWpl2Pf22PcPe4KklebM6yLE82w== 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=34gjvjvZYDTksl2mvj87AN1/sVXlfDbDB1ksAZEScAc=; b=X7l3GS/pA0V35R52YF/XPe67n2z/vkQvhhe7qLWZnkr+Zz9FKgLdaqv3s7aHogxm/e1yx3/mkHIhYoZDIeEfbpwjItY08oeCXzcjo6ZFKTLSJFjy9nLWj1QDbvszTIghqaph+jrBhd1SM2e/SjovwZ7zoMffcGg5XnMZ5bOeuzsJGusf6rOa9rE7FHkmjVIPqNEyGOa3D9fxKRCB2TeXlDeIZl6QfhEIco6uSyKHKx++iot5q6SJ0ZzO0iEIpn0mR2auOVLEzaA9JFc/CAz7M6871UIBiN6vBNZ+q2U5UEGiZamziJoAOWzH43MtEnRKRe/At1ZGhZBnckGKiluPFQ== ARC-Authentication-Results: i=4; mx.microsoft.com 1; spf=pass (sender ip is 52.101.56.11) smtp.rcpttodomain=mq.edu.au smtp.mailfrom=ksu.edu; dmarc=bestguesspass action=none header.from=ksu.edu; dkim=fail (body hash did not verify) header.d=ksu.edu; arc=pass (0 oda=0 ltdi=0 93) Received: from SYBPR01MB6745.ausprd01.prod.outlook.com (2603:10c6:10:12c::10) by SYBPR01MB5757.ausprd01.prod.outlook.com (2603:10c6:10:9f::6) with Microsoft SMTP Server (version=TLS1_2, cipher=TLS_ECDHE_RSA_WITH_AES_256_GCM_SHA384) id 15.20.7249.34; Mon, 5 Feb 2024 00:48:53 +0000 Received: from MEAPR01MB3654.ausprd01.prod.outlook.com (2603:10c6:201:38::9) by SYBPR01MB6745.ausprd01.prod.outlook.com (2603:10c6:10:12c::10) with Microsoft SMTP Server (version=TLS1_2, cipher=TLS_ECDHE_RSA_WITH_AES_256_GCM_SHA384) id 15.20.7249.34; Mon, 5 Feb 2024 00:48:50 +0000 Received: from MEAPR01MB3654.ausprd01.prod.outlook.com ([fe80::8d2b:eb3:c473:3596]) by MEAPR01MB3654.ausprd01.prod.outlook.com ([fe80::8d2b:eb3:c473:3596%7]) with mapi id 15.20.7249.032; Mon, 5 Feb 2024 00:48:50 +0000 ARC-Seal: i=3; a=rsa-sha256; s=arcselector9901; d=microsoft.com; cv=pass; b=m0lTOB16CAinMm4kBqnevFfLL4yOkokWK43HP66cZ1OxWxSLqrzXLR97HRiF1oVlTYxjZCHoyoR575luTQeX8JhaUcgVh/Gl/qP3wh0Mg0V1FOWi/wpbrrDtHrNXnxzNmq9BSZM+RvfkSQsZcsl8Z4lo8KabP74q5njrGn+pa7NCL5bq3TRfjsP5qi22koBJ3iO8IJ5vKGzhG/3ZITFOFv76FCXRqo1k0RbGzZVrT2bX9scz9PTlNjwKXeKK2V5zeRAEKzC2vHn+7bCOH2/R8ZXWHYvlnlU8u+zRz1uw6sik8utowvWsnlN4dmrHlcALuFy+bL7sFLsuNZhQ8rrk1A== 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=34gjvjvZYDTksl2mvj87AN1/sVXlfDbDB1ksAZEScAc=; b=Hp4x42scmQNgn/NI6WqWQegLgO4ODfAZIp18KKuQEYaaFZgnd1kLgSm4oRHneru8efCpCiqW9ywmwDbOu9FHW9SCxqfxr0MCBZLrjfi0BvdT0wShXA9yWF6iM9TiHwcf6qmEK6VZyVL3+Kf/7vRRZfLUzdPraCDgOlcESlNv8CzLmQiPGRuFRjSSG0cPJbrtasZywtk4N8C2xeM+4DX26JJJnaLLckpcOflRU0G2w5hiQ/AaqIWFQZ0MRs3mouS1sYI/h337GfwLOmkgsYWGsSk8CwrBxY+Po9SEyunNufQDe7Wr31M5n8BLCIjDLZOzup4OrihTxmQo78g5mjWNrg== ARC-Authentication-Results: i=3; mx.microsoft.com 1; spf=pass (sender ip is 52.101.56.11) smtp.rcpttodomain=mq.edu.au smtp.mailfrom=ksu.edu; dmarc=bestguesspass action=none header.from=ksu.edu; dkim=fail (body hash did not verify) header.d=ksu.edu; arc=pass (0 oda=0 ltdi=0 93) Received: from MEWPR01CA0123.ausprd01.prod.outlook.com (2603:10c6:220:1d3::20) by SYBPR01MB7994.ausprd01.prod.outlook.com (2603:10c6:10:1a1::5) with Microsoft SMTP Server (version=TLS1_2, cipher=TLS_ECDHE_RSA_WITH_AES_256_GCM_SHA384) id 15.20.7249.34; Mon, 5 Feb 2024 00:01:03 +0000 Received: from ME3AUS01FT021.eop-AUS01.prod.protection.outlook.com (2603:10c6:220:1d3:cafe::6e) by MEWPR01CA0123.outlook.office365.com (2603:10c6:220:1d3::20) with Microsoft SMTP Server (version=TLS1_2, cipher=TLS_ECDHE_RSA_WITH_AES_256_GCM_SHA384) id 15.20.7249.34 via Frontend Transport; Mon, 5 Feb 2024 00:01:03 +0000 Authentication-Results: spf=pass (sender IP is 52.101.56.11) smtp.mailfrom=ksu.edu; dkim=fail (body hash did not verify) header.d=ksu.edu;dmarc=bestguesspass action=none header.from=ksu.edu; Received-SPF: Pass (protection.outlook.com: domain of ksu.edu designates 52.101.56.11 as permitted sender) receiver=protection.outlook.com; client-ip=52.101.56.11; helo=BN1PR04CU002.outbound.protection.outlook.com; pr=C Received: from au-smtp-inbound-delivery-1.mimecast.com (103.96.22.101) by ME3AUS01FT021.mail.protection.outlook.com (10.114.155.143) with Microsoft SMTP Server (version=TLS1_3, cipher=TLS_AES_256_GCM_SHA384) id 15.20.7249.30 via Frontend Transport; Mon, 5 Feb 2024 00:01:02 +0000 ARC-Message-Signature: i=2; a=rsa-sha256; c=relaxed/relaxed; d=dkim.mimecast.com; s=201903; t=1707091262; h=from:from:reply-to:subject:subject:date:date:message-id:message-id: to:to:cc:mime-version:mime-version:content-type:content-type: dkim-signature; bh=34gjvjvZYDTksl2mvj87AN1/sVXlfDbDB1ksAZEScAc=; b=ZKKuwjuWYtfo4jZZqCIoql2WesCvFOln8TrW/XnnQiOckTOdD0uyRjqztGh3DwmmzbIAz9 yugWdscDU+XXD5eaF/W6vVrq6Xf6N5IoA0ev3QGyptO4E69m1FTLlmhN+ZrNyJz/y6i6pG zPu7naVgP556OjBGlkenIqb3r1rBuXZrIw+44myD9CkbqHq0hRHGFLNjRAxyvRIErCyMcE /wzJqD5lBvCL+Gdh0pPzGZGU+q99RsCpjId6MnsQRTh7zwj4Ck+sCufDSXiqgVWCIF7nAR t8C9FJRph3rXmJaHOvPrIpK7Zs7jq+rQ4I9GZKF7WUkUBT0nKbE6/swMNDUfug== ARC-Seal: i=2; s=201903; d=dkim.mimecast.com; t=1707091262; a=rsa-sha256; cv=pass; b=dUXgnuQOFM6JCdmioadvBWtkf9eZlCYTZnHCAofpc0XwAgTCo+6LgQXNQsU8QNZ+AUvh6T kCicS+M+bqt0Ev7uuPWwC4Gh39nPXbrdSNp6wZ7HlHx4AotL6pdOufr1MZDdWI9o2g8KWq 2k66PWjhHuCNA4tKpaGLqE3O12FOs5MoT81OETWX4NKwgh+VlmPNtdeZg628LuW+ByiSrG XW8wwA0MOIUwaZcuPHyU+ozRKj5DsyRt5g5fayyxbJDbz5vAtPs8qys4kixoIIbilmUmuQ RgORBVcjB6qcRm0MU+g/rGPEq7Y+e3C1zOGbLMWixNV+ySYBufv/flVQBaAhgg== ARC-Authentication-Results: i=2; relay.mimecast.com; dkim=pass header.d=ksu.edu header.s=selector1 header.b=xzC3DuvF; arc=pass ("microsoft.com:s=arcselector9901:i=1"); dmarc=pass (policy=none) header.from=ksu.edu; spf=pass (relay.mimecast.com: domain of dyetter@ksu.edu designates 52.101.56.11 as permitted sender) smtp.mailfrom=dyetter@ksu.edu Received: from BN1PR04CU002.outbound.protection.outlook.com (mail-eastus2azon11022011.outbound.protection.outlook.com [52.101.56.11]) by relay.mimecast.com with ESMTP with STARTTLS (version=TLSv1.2, cipher=TLS_ECDHE_RSA_WITH_AES_256_GCM_SHA384) id au-mta-96-38yO-tfHNEuA0lqIY3MRuA-1; Mon, 05 Feb 2024 11:00:59 +1100 X-MC-Unique: 38yO-tfHNEuA0lqIY3MRuA-1 ARC-Seal: i=1; a=rsa-sha256; s=arcselector9901; d=microsoft.com; cv=none; b=Ga962kunIb1hZEMzIxKcFI441bQ4k6oHmydhEu0y4gdzo2Lwrv0XvciMmKLbIDagZ4tG34XVT6ilbSgCL+mUL4ZxVhtERPMb1dnP18WRX/uN8rJXEYMmRU0H+0gLl3To4EQ4rNqMHBWCOWhX4z4g3C5UEeP+WgufB273WmLvN+F/kyPiGNyo6ngKpf8t8VtwkNu2YKdnwEx5VQoFPU8D3l4YuSYbCtZuWY1GqON0jNw9uhzizZmtHbCiiOaF+bjVg083YRWZQAjAVDICn60lTWo/WTQmZfZ9/W+zMkedbSP4IYVS7O+8Fs64H23jNiCeH+pZn3VUa8DN7ANFoWe/0A== ARC-Message-Signature: i=1; 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=5OUM9Wk7zaYM6vhDkVUOfU+kVCqZKi6ig9gRHFSTb7g=; b=htnMjQ8B9FlZC1PqOTOyjNdbMis/Ej18JD8FwZIpJ/Xl0RoU9Xx6mW9ubFrr+owLLEwhBS6QSKo/KuU8P3ABYuwJCLDsS6+r1HpgKHm2fQCiVw4l5e7P7xQYmr5+LrbuZBmBxwLh6ogl7AMoOkWVPDhlG8guPMi4i41mXgqSFy+VWZwlud4Fe/fDnGYY1Aog2SvSbewlvK3mduM96H7bwVAYAGnOopGxoaKrB4CGLfBQxJBKfinem2oovT3MoaI0/tifR91m+KN8KhPqOH81BVx1R5Hxq1OrmqSz2hTh1F7lJxPtNh3d/KzaOkyLkvFvJXCRydVT4o+vXtoOg6fHZw== ARC-Authentication-Results: i=1; mx.microsoft.com 1; spf=pass smtp.mailfrom=ksu.edu; dmarc=pass action=none header.from=ksu.edu; dkim=pass header.d=ksu.edu; arc=none DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=ksu.edu; s=selector1; h=From:Date:Subject:Message-ID:Content-Type:MIME-Version:X-MS-Exchange-SenderADCheck; bh=5OUM9Wk7zaYM6vhDkVUOfU+kVCqZKi6ig9gRHFSTb7g=; b=xzC3DuvFXrCyoHmDLrOtKYLFwZgwTOOPgDW9VkJEyJFHQO8pX0XiAASYIMzV/tJOFdi9VgUSZbbs7Vn/5UndV14y9nBf/IMOpptBautWCictwl11lHoLhGt8kXWhxYuzKxddcpkcZFfE1Nyp48XEYkkcdFgKeJKCzpkr273h3c8= Received: from SN6PR05MB5213.namprd05.prod.outlook.com (2603:10b6:805:df::28) by CY8PR05MB10156.namprd05.prod.outlook.com (2603:10b6:930:6f::12) with Microsoft SMTP Server (version=TLS1_2, cipher=TLS_ECDHE_RSA_WITH_AES_256_GCM_SHA384) id 15.20.7249.34; Mon, 5 Feb 2024 00:00:54 +0000 Received: from SN6PR05MB5213.namprd05.prod.outlook.com ([fe80::78ac:6776:2b9c:3786]) by SN6PR05MB5213.namprd05.prod.outlook.com ([fe80::78ac:6776:2b9c:3786%6]) with mapi id 15.20.7249.032; Mon, 5 Feb 2024 00:00:54 +0000 From: David Yetter To: "categories@mq.edu.au" Subject: Monadicity questions Thread-Topic: Monadicity questions Thread-Index: AQHaV8Qu9MisEtaiTUKPrcyCtrsOxw== Date: Mon, 5 Feb 2024 00:00:54 +0000 Message-ID: Accept-Language: en-US X-MS-Has-Attach: X-MS-TNEF-Correlator: msip_labels: x-ms-traffictypediagnostic: SN6PR05MB5213:EE_|CY8PR05MB10156:EE_|ME3AUS01FT021:EE_|SYBPR01MB7994:EE_|SYBPR01MB6745:EE_|SYBPR01MB5757:EE_ X-MS-Office365-Filtering-Correlation-Id: 6fb37d20-208f-44b4-1c24-08dc25dd8adc X-MS-Exchange-SenderADCheck: 0 X-MS-Exchange-AntiSpam-Relay: 0 X-Microsoft-Antispam-Untrusted: BCL:0 X-Microsoft-Antispam-Message-Info-Original: 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 X-Forefront-Antispam-Report-Untrusted: CIP:255.255.255.255;CTRY:;LANG:en;SCL:1;SRV:;IPV:NLI;SFV:NSPM;H:SN6PR05MB5213.namprd05.prod.outlook.com;PTR:;CAT:NONE;SFS:(13230031)(366004)(39860400002)(396003)(376002)(136003)(346002)(230922051799003)(64100799003)(186009)(1800799012)(451199024)(55016003)(33656002)(41300700001)(66899024)(19627405001)(75432002)(9686003)(86362001)(38070700009)(478600001)(2906002)(3480700007)(83380400001)(26005)(5660300002)(64756008)(7116003)(66946007)(66446008)(6506007)(786003)(71200400001)(38100700002)(66556008)(316002)(52536014)(66476007)(122000001)(296002)(76116006)(6916009)(8936002)(8676002)(7696005);DIR:OUT;SFP:1102 MIME-Version: 1.0 X-MS-Exchange-Transport-CrossTenantHeadersStamped: CY8PR05MB10156 Authentication-Results-Original: relay.mimecast.com; dkim=pass header.d=ksu.edu header.s=selector1 header.b=xzC3DuvF; arc=pass ("microsoft.com:s=arcselector9901:i=1"); dmarc=pass (policy=none) header.from=ksu.edu; spf=pass (relay.mimecast.com: domain of dyetter@ksu.edu designates 52.101.56.11 as permitted sender) smtp.mailfrom=dyetter@ksu.edu 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=false;Mimecast Threat Dictionary=false;Custom Threat Dictionary=false Content-Language: en-US Content-Type: multipart/alternative; boundary="_000_SN6PR05MB5213D1A72C5E6648F21E2BBAA2402SN6PR05MB5213namp_" X-EOPAttributedMessage: 0 X-EOPTenantAttributedMessage: 82c514c1-a717-4087-be06-d40d2070ad52:0 X-MS-Exchange-SkipListedInternetSender: ip=[52.101.56.11];domain=BN1PR04CU002.outbound.protection.outlook.com X-MS-Exchange-ExternalOriginalInternetSender: ip=[52.101.56.11];domain=BN1PR04CU002.outbound.protection.outlook.com X-MS-Exchange-Transport-CrossTenantHeadersStripped: ME3AUS01FT021.eop-AUS01.prod.protection.outlook.com X-MS-PublicTrafficType: Email X-MS-Office365-Filtering-Correlation-Id-Prvs: c4c854d8-934b-45f6-2488-08dc25dd85ff X-Moderation-Data: 2/5/2024 12:48:47 AM X-LD-Processed: 82c514c1-a717-4087-be06-d40d2070ad52,ExtAddr,ExtAddr X-MS-Exchange-AtpMessageProperties: SA X-Microsoft-Antispam: BCL:0; X-Microsoft-Antispam-Message-Info: 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 X-Forefront-Antispam-Report: CIP:103.96.22.101;CTRY:US;LANG:en;SCL:1;SRV:;IPV:NLI;SFV:NSPM;H:BN1PR04CU002.outbound.protection.outlook.com;PTR:mail-eastus2azon11022011.outbound.protection.outlook.com;CAT:NONE;SFS:(13230031)(4636009)(136003)(396003)(376002)(39860400002)(346002)(82310400011)(8000799017)(48200799006)(451199024)(61400799012)(64100799003)(40470700004)(86362001)(498600001)(9686003)(41110700001)(32650700002)(40460700003)(40480700001)(55016003)(76576003)(88732003)(336012)(19627405001)(89122003)(156005)(26005)(6506007)(7696005)(35950700001)(32850700003)(83380400001)(82740400003)(7636003)(3480700007)(316002)(786003)(6862004)(8936002)(8676002)(33656002)(75432002)(52536014)(7116003)(66899024)(5660300002)(7276002)(7336002)(7406005)(7416002)(7366002)(41300700001)(2906002)(70586007)(68406010)(17680700008)(41090700016)(41080700001);DIR:OUT;SFP:1501; X-Auto-Response-Suppress: DR, RN, NRN, OOF, AutoReply X-MS-Exchange-CrossTenant-Network-Message-Id: 6fb37d20-208f-44b4-1c24-08dc25dd8adc X-MS-Exchange-CrossTenant-Id: 82c514c1-a717-4087-be06-d40d2070ad52 X-MS-Exchange-CrossTenant-AuthSource: ME3AUS01FT021.eop-AUS01.prod.protection.outlook.com X-MS-Exchange-CrossTenant-AuthAs: Anonymous X-MS-Exchange-CrossTenant-FromEntityHeader: Internet X-MS-Exchange-CrossTenant-OriginalArrivalTime: 05 Feb 2024 00:48:50.0686 (UTC) X-MS-Exchange-CrossTenant-MailboxType: HOSTED X-MS-Exchange-CrossTenant-UserPrincipalName: W5xg/2PCndyrFkvNNgX93eUNNgLP0UkGAA7oJ/0KbvcvED6bN+RQ/m2nFxENggXses+BcoS63i7gg5ZvLn7HSTFIf3zlkOnSwRd8yoP+qTE0UY3QntnlxOEh5zf9xG4YHFxoSeM2jxsPEvh5QNFdtIin4G+6PvZ0P99eOOX0MgeKZddDVuNpQ+/a9H6PKvrq1h1xDgUTXb6+BlJU3YRwzkvalP5evmNls8kMSiWoM+w= X-MS-Exchange-Transport-CrossTenantHeadersStamped: SYBPR01MB5757 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: =?Windows-1252?Q?qhZiWhfOgHd+j+Ac4aZlXUFsDlqs7Ihq1j0hCPgl4IOYizAbQKmS0jYf?= =?Windows-1252?Q?lpzyxwZ/TWqw+HyuiCKLXA1pF8ghWjE2CdsznDllX7Tco1Bn+l7Pb+eE?= =?Windows-1252?Q?fJi+JzC/WAwLLij2SIsNuQPiLplrTZ5QEh+I3ODqXL8U43I1bL55kOCt?= =?Windows-1252?Q?KI5mHMpHS6BJY8InjE2fNWpQMw6nbrIUkm8vUZqeCDwGY5J6S3Jzb0Iw?= =?Windows-1252?Q?EqZ3u6bJYT3Uh/OsKjdjgIqKiNIFkjB1Y1K1Bk8dcuN9nnzjFSEYNlF8?= =?Windows-1252?Q?elj9AN0O3rPHi5QMAJr1l/xF6IqogJ5Vz4lRuAPw9PmW5nmYKbbZFwHI?= =?Windows-1252?Q?cbtFc2sA4mmnbRCVDxN3ZH50Cq3yQJJu6XF9SmyiS0nS4LZffyERb6iw?= =?Windows-1252?Q?tcqc2xsxck65gy4l8mzZrsDqSNAp/OAfY85jwuT0wA75k5E6whya/v0G?= =?Windows-1252?Q?RG5kFRoALtmwAYa9NF9iwDYHlqGViHvKuZIhJk2M/f1t/iuYE+E+jFyr?= =?Windows-1252?Q?JOpkKXFzYdVxnjkreLrvYg/2VbHS/MDMSAZ8FN6dUQiv7GI8+YFgtjAB?= =?Windows-1252?Q?2levYV0lgixhyfLuOr5edS7cFEWTJg47HgtirlFewfYlNbQUwR16qulQ?= =?Windows-1252?Q?g6woWp9IcuHbfKWJplcYOyuuL9dxyHcNcGKNsSPaK+YfvX4ufHlxdk4b?= =?Windows-1252?Q?xa8ERVzW40JLR91ZRW86AduKMVOtaIZNIH/INI2OwBhVvWn9DYo0ft9o?= =?Windows-1252?Q?a8ye5xb3Z0LiJHv+mYfT2+abZByrTESBXQgwF47gCCjdAw+xN4PAaR0u?= =?Windows-1252?Q?M5v2Ks+u9Pp4JcNVioHBSNZmkKMzxjBoLCYk6gK42ZvKHI+1+/R4k8dw?= =?Windows-1252?Q?yQyyQ8XygZCBOwaw7Jl7lVTeAHgV3Kudd3Zx/nMD2izYMsSR4QL7fKQm?= =?Windows-1252?Q?WzGkIXTOa1gEK/vxF8CHmEXMZNYti0eY8NoY5ZCtJ2SrWTDfFiwx3trO?= =?Windows-1252?Q?83md+v5TXu+erVlQjVUckxpmmXxVa7A+jIMl10q7YJJeBs8jBsPfMtrl?= =?Windows-1252?Q?M+ron+lk4SUQkWgObCSItuLXSSEtwKs4KdkbTbuCgyW3aDMLkAZlpLgL?= =?Windows-1252?Q?z/RQJ6VNFMdNxpfSQzOBPoxaVzUryhZghSj6RK5FvAgIWuzF6Zbwomsn?= =?Windows-1252?Q?olbUUk/FAHpsySkAd4ueirpceOO8qYG4p1dHr+/noUNs1DUUsJX3W1nu?= =?Windows-1252?Q?XZNkWFdgp5l881+uVF23QCCEbAS7BLwlVifPP9rsoHpv0gpbrF88jFIe?= =?Windows-1252?Q?tXl0fQ/UV98HQujDaoDNo6n9vYpABeJnNBv2enDGICoTJ7/AJfZIslW9?= =?Windows-1252?Q?9ISegmHSH12w23xHfEC3WgZGNi66ENdzYWU=3D?= X-OriginatorOrg: mq.edu.au --_000_SN6PR05MB5213D1A72C5E6648F21E2BBAA2402SN6PR05MB5213namp_ Content-Type: text/plain; charset="Windows-1252" Content-Transfer-Encoding: quoted-printable We are all, of course, familiar with Beck's Theorem. I'm rather hoping tha= t there are results in the literature that will save me from having to prov= e that the underlying functor U creates coequalizers for U-split pairs in t= he context of two quite different projects I'm working on. Thus, I have tw= o questions for the community: 1. It seems obvious to me that for the same reason categories of models of fin= itary algebraic (equational) theories are monadic over Set, if one has (I t= hink I'm using the term correctly here) a conservative extension of an equa= tional theory (by which I mean, add operations and equations in such a way = that no new equations are imposed on the operations of the original theory)= , then the category of models of the extension is monadic over the category= of models of the original theory. Surely this is either explicitly stated= and proved somewhere, or follows easily from some result I simply have not= encountered. Citations? 2. What is the most general sort of theory whose models are monadic ove= r Set? Or if that is not known, what sorts of theories have monadic categor= ies of models over Set? Are there multisorted generalizations of any resu= lts of that sort, ideally not just to Set^\alpha, where \alpha is the cardi= nality of a set of sorts, but to things like Graph? Again some citations w= ould be much appreciated. Best Thoughts, David Yetter University Distinguished Professor Department of Mathematics Kansas State University (That is the first and last time I'll use that signature block in writing t= o the list, but I thought I'd do it once since I thought the community woul= d be gratified that a categorist was so honored. After this it's back to D= avid Y. or D.Y.) 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 --_000_SN6PR05MB5213D1A72C5E6648F21E2BBAA2402SN6PR05MB5213namp_ Content-Type: text/html; charset=WINDOWS-1252 Content-Transfer-Encoding: quoted-printable
We are all, of course, familiar with Beck's Theorem.  I'm rather hopin= g that there are results in the literature that will save me from having to= prove that the underlying functor U creates coequalizers for U-split pairs= in the context of two quite different projects I'm working on.  Thus, I have two questions for the communit= y:

  1. It seems obvious to me that for the same reason = categories of models of finitary algebraic (equational) theories are monadic over Set, if one has (I think I'm using = the term correctly here) a conservative extension of an equational the= ory (by which I mean, add operations and equations in such a way that no ne= w equations are imposed on the operations of the original theory), then the category of models of the extension is m= onadic over the category of models of the original theory.  Surely thi= s is either explicitly stated and proved somewhere, or follows easily from = some result I simply have not encountered.   Citations?
  2. &nb= sp;What is the most general sort of theory whose models are monadic over Se= t? Or if that is not known, what sorts of theories have monadic categories of models over Set?   Are th= ere multisorted generalizations of any results of that sort, ideally not ju= st to Set^\alpha, where \alpha is the cardinality of a set of sorts, but to= things like Graph?  Again some citations would be much appreciated.

Best Thoughts,
David Yetter
University Distinguished Professor
Department of Mathematics
Kansas State University

(That is the first and last time I'll use that s= ignature block in writing to the list, but I thought I'd do it once since I thought the community would be gratif= ied that a categorist was so honored.  After this it's back to David Y= . or D.Y.)

 
 
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
 
--_000_SN6PR05MB5213D1A72C5E6648F21E2BBAA2402SN6PR05MB5213namp_--