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From: Thomas Streicher <streicher@mathematik.tu-darmstadt.de>
To: Jon Sterling <jon@jonmsterling.com>
Cc: Christian Sattler <sattler.christian@gmail.com>,
	Richard Garner <richard.garner@mq.edu.au>,
	David Roberts <droberts.65537@gmail.com>,
	"categories@mq.edu.au" <categories@mq.edu.au>
Subject: Re: Fibrewise opposite fibration
Date: Thu, 1 Feb 2024 12:46:08 +0100	[thread overview]
Message-ID: <ZbuEgFJbk/8k4IvY@mathematik.tu-darmstadt.de> (raw)
In-Reply-To: <7522ed21-1c0f-4601-8038-b7c7586d704f@app.fastmail.com>

> I'm sympathetic, but I don't agree about the comparison to vector spaces because a cleaving is nothing like a basis. My evidence for this is that for fibrations of univalent categories, cleavings are always canonical; on the other hand, there is no foundational tweak that could make vector spaces have canonical bases.

I agree that from a univalent point of view all cleavages are equal.
But from a univalent point of view all cleavages are even split!
That is a bit too much for me (see Warning (1) on p.10 of my notes on
fibered cats).

But I do not want to take up old discussions! I really prefer to disagree.

Instead I admit that all choices of cleavages are uniquely isomorphic
which certainly is not teh case for bases.

Thomas



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  reply	other threads:[~2024-02-01 20:11 UTC|newest]

Thread overview: 33+ messages / expand[flat|nested]  mbox.gz  Atom feed  top
2024-01-28  0:51 David Roberts
2024-01-28 11:54 ` Jon Sterling
2024-01-28 20:03   ` Thomas Streicher
2024-01-30  6:42     ` David Roberts
2024-01-31  0:35       ` Richard Garner
2024-01-31 19:31         ` Christian Sattler
2024-01-31 23:41           ` streicher
2024-02-01  4:48             ` Martin Bidlingmaier
2024-02-01  9:43             ` Jon Sterling
2024-02-01 11:06               ` Thomas Streicher
2024-02-01 11:18                 ` Jon Sterling
2024-02-01 11:46                   ` Thomas Streicher [this message]
     [not found]                     ` <ZbuFZoT9b9K8o7zi@mathematik.tu-darmstadt.de>
2024-02-02 10:11                       ` Thomas Streicher
2024-02-01 11:26                 ` Christian Sattler
2024-02-09  0:02 ` Dusko Pavlovic
2024-02-09  1:48   ` Michael Barr, Prof.
2024-02-09 19:55     ` Dusko Pavlovic
2024-02-10  6:28       ` David Roberts
2024-02-10  8:42         ` Jon Sterling
2024-02-09 11:25   ` Fibrewise opposite fibration + computers Sergei Soloviev
2024-02-09 20:25     ` Dusko Pavlovic
2024-02-12 13:20   ` Fibrewise opposite fibration Nath Rao
2024-02-13  8:16     ` Jon Sterling
2024-02-13 10:04       ` Thomas Streicher
2024-02-13 10:56         ` Jon Sterling
2024-02-13 11:38           ` Thomas Streicher
2024-02-13 11:53             ` Jon Sterling
2024-02-13 12:18               ` Thomas Streicher
2024-02-13 16:35                 ` Thomas Streicher
2024-02-23  1:50                   ` Dusko Pavlovic
2024-02-23  1:52                     ` Dusko Pavlovic
2024-02-23  1:42     ` Dusko Pavlovic
2024-02-26  7:31       ` Dusko Pavlovic

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