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X-Auto-Response-Suppress: DR, OOF, AutoReply X-MS-Exchange-CrossTenant-Network-Message-Id: 237a9c48-27f1-4808-2591-08dc22b64061 X-MS-Exchange-CrossTenant-Id: 82c514c1-a717-4087-be06-d40d2070ad52 X-MS-Exchange-CrossTenant-AuthSource: ME3AUS01FT015.eop-AUS01.prod.protection.outlook.com X-MS-Exchange-CrossTenant-AuthAs: Anonymous X-MS-Exchange-CrossTenant-FromEntityHeader: Internet X-MS-Exchange-CrossTenant-OriginalArrivalTime: 31 Jan 2024 23:45:13.1189 (UTC) X-MS-Exchange-CrossTenant-MailboxType: HOSTED X-MS-Exchange-CrossTenant-UserPrincipalName: KcbZzr2Xaqe4HAc4uSYgRGs5S6gsMByEGlZkMPEeKUNQyeytOpQnw0DV7C7U7BiVYnuEM4NRrbMi6Yn4dsOuDmXl94C/Bp1VCyiz4OygKjCCcuyc3Rm2O/xiWP8vGnvcsS1OnECYe66z/I1E1FzNztML6nXBQ0fV8OIqVxNgVDirSNNGL21fDcQoLHHOMbMv X-MS-Exchange-Transport-CrossTenantHeadersStamped: SY4PR01MB5850 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: <5aca1a1590406e68498c51bb858d89b5.squirrel@webmail.mathematik.tu-darmstadt.de> 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?BAdYKrwVUosGtSkyIfV7UxcCuIrQFfVJ3SAFOHiGtnf1RJDwgJTEpDy4?= =?Windows-1252?Q?tZKKxEdxkV8vPbn8pBfLxjR2y5hvuYQI5FJwRcGjcssKdqZxfGv395OA?= =?Windows-1252?Q?8eVfPvKVxl1hkA3bZ8E461Zs5fXTytE3MK+3NQPHSj4HxLXZR3THepk4?= =?Windows-1252?Q?1CPA3VzUMlhuY+xY6QRURH7oeYtB55Hd9ZSLe26uGYXhiK2rdn2Wj0Ba?= =?Windows-1252?Q?u0U2UDOYowODPUPCRRvLKBnBXMgR8urlmZHjX+EIxgTnSY0Nv5Xu9UN8?= =?Windows-1252?Q?/7fmjFRwq/Aq9P9lL7xPBXz1UueUaefMWfGBiI8tk6enSepnuNUVmVPn?= =?Windows-1252?Q?FwbhPCRRzum5nbUP52E9iBn7VP36fJRhYLsMgSN2Xj0o0b3BjyYcmjpl?= =?Windows-1252?Q?bTHs0OlAoGD8zrTgQ8oMziwSwIMG7rRqExClszG1dyhr/iRZkmBFVbyq?= =?Windows-1252?Q?SJEbUhj7HpPh2wq6IRTDyXES/ZO2xTB1iaPswT5Bzc899ilLxuDmfrCA?= =?Windows-1252?Q?dICI0vvthnsZpxuWtQMhIiCKxwF05grwTzPHyFcNnvZ7Bc8GyOutaTBF?= =?Windows-1252?Q?zxaCEeHwZTW+cY2U6hJnWFmtMqno36vr1/7cDVp4sTbjU3kRd3jKJO9d?= =?Windows-1252?Q?aQj8k/XSYcADM4tjOZUZoEnmJ4sDMOgQ7666Hu6/k7CCDPvCSw9AvWRu?= =?Windows-1252?Q?EkfkezXvzIMf8ZTQ/5mWFVsXvgyh5J1hbZBJftcBIU6zDOxnjS0VHN8j?= =?Windows-1252?Q?pqu6rOQx23Gr6pkfLHm/ZY0K0phzi/OyRBmJFznaVnEBTRt+iIvwsjfh?= =?Windows-1252?Q?YHkkM0AL7mUOFnS8v7V7eTWUwUngOxNlvDV1gcLFpsJ8kqjaon94IEuw?= =?Windows-1252?Q?nJ/B7WECv7Xd/LASSrzdbkw7+0WA/NhveYqSJ/jD4/mnKFhDG8/1jqPz?= =?Windows-1252?Q?KT7TNrEa+LMjJZ9K5jrskBx1UcALvoiVM1I+5/yN72lA7R9qJkq96Hq/?= =?Windows-1252?Q?w+keP9QKiruP3N9Smz+R/z6fnoCw0D6x4W0e64i2y6S31EPgMMkuRcoM?= =?Windows-1252?Q?+/zEQILYryc6q1h1bpavFnHVNen38w6eoFabfZF5GqocfcgVihsaiaUA?= =?Windows-1252?Q?hwflq76FqD83k4YOHoHqoryHKdip4FNKZxQjpiSPeKLyRAKKvUq4+2rD?= =?Windows-1252?Q?Ai535g+5FCih5+SmU4ydeAyMkgt1P+QLU2oupmnHDN4yPttfFuI54xIj?= =?Windows-1252?Q?zE7RFhFYKPhwm/LvFmMrt/ba1TP5WOQ9wXO3SgEnJQh2Lz7Cgv2Kmkeb?= =?Windows-1252?Q?yQMvHGw2nxD8YbA6FTKOv8YDo0Bh6BD+6PcBdHmUGLsSTheRXOfxj13v?= =?Windows-1252?Q?ytZTDxJeKgQSjiFxt5FlqmjqqzEItKvs/wgXOBso1H++EqxXUTs5grdP?= =?Windows-1252?Q?awSrb9WBOMsmb8URreBd5nXGS3U20p/bSlIwO1AVgvKqToE+DK5uIIYK?= =?Windows-1252?Q?IbYWi9bGyRih747XI8/9OMubF/UOyPss1Of45laPaVfdBWN4VFiqCqnY?= =?Windows-1252?Q?baiuidaK4Jpmhgru?= X-OriginatorOrg: mq.edu.au If we work with split fibrations and arbitrary cartesian functors between them we can construct the opposite of a fibration without quotienting. That is possible but in my eyes less elegant than the usual approach where one assumes that one can factorize modulo equivalence relations even if they are big. Thomas ---------- You're receiving this message because you're a member of the Categories mai= ling list group from Macquarie University. Leave group: https://outlook.office365.com/owa/categories@mq.edu.au/groupsubscription.as= hx?source=3DEscalatedMessage&action=3Dleave&GuestId=3D4eb9b40c-9b3a-48a5-97= 81-836e5a171e8b