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 12:06:59 +0100 [thread overview]
Message-ID: <Zbt7UxPYa9DSxx2x@mathematik.tu-darmstadt.de> (raw)
In-Reply-To: <d767a725-8c2b-46ac-8575-a77e3abe607e@app.fastmail.com>
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 20:09 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 [this message]
2024-02-01 11:18 ` Jon Sterling
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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