From: "Jon Sterling" <jon@jonmsterling.com>
To: "Thomas Streicher" <streicher@mathematik.tu-darmstadt.de>
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, 01 Feb 2024 11:18:16 +0000 [thread overview]
Message-ID: <7522ed21-1c0f-4601-8038-b7c7586d704f@app.fastmail.com> (raw)
In-Reply-To: <Zbt7UxPYa9DSxx2x@mathematik.tu-darmstadt.de>
Hi Thomas,
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.
Best,
Jon
On Thu, Feb 1, 2024, at 11:06 AM, Thomas Streicher wrote:
> Dear Jon,
>
> for constructing the opposite of a fibration you do not need at all
> that the chosen cleavage is split. It is easy to see that fixing the
> cartesian arrow also fixes the vertical arrow.
>
> If everybody is happy with this solution I am fine. It is in the same spirit
> as chosen pullbacks or chosen finite limits.
> The reason for my reluctance is that nobody would consider as a
> natural notion a vector space with a chosen basis.
> The virtue of strong choice is that then such additional structure can be
> pulled out of the hat at demand.
>
>
> Thomas
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next prev parent reply other threads:[~2024-02-01 20:10 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 [this message]
2024-02-01 11:46 ` Thomas Streicher
[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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