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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next prev parent 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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