From: Thomas Streicher <streicher@mathematik.tu-darmstadt.de>
To: Vaughan Pratt <pratt@cs.stanford.edu>
Cc: Wesley Phoa <doctorwes@gmail.com>,
Francis Borceux <francis.borceux@uclouvain.be>,
categories@mq.edu.au
Subject: Re: Sorry
Date: Wed, 24 Jan 2024 12:02:13 +0100 [thread overview]
Message-ID: <ZbDuNT+RXihZULtf@mathematik.tu-darmstadt.de> (raw)
In-Reply-To: <CAL7kZqAKbUasCdSkX=c1fQk3dqhDC2oiw+VCUD28D-22zwWK7w@mail.gmail.com>
Dear Vaughan,
Benabou"s JSL paper is certainly more of a philosophical character
than a mathematical one. But philosophical issues can be relevant and
in this case definitely are.
I think the following analogy might be helpful. Using strong choice
principles every vector space can be endowed with a basis. But nobody
thinks that they should form part of the definition or even be preserved
by morphisms between them.
And so it is with Grothendieck fibrations. They are the right notion
but one may choose cleavages. However, they are not part of the structure
and certainly should not be preserved by morphism, i.e. cartesian functors.
Thomas
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next prev parent reply other threads:[~2024-01-24 20:31 UTC|newest]
Thread overview: 8+ messages / expand[flat|nested] mbox.gz Atom feed top
2024-01-22 12:21 Sorry Francis Borceux
2024-01-22 20:19 ` Sorry Wesley Phoa
2024-01-24 8:08 ` Sorry Vaughan Pratt
2024-01-24 11:02 ` Thomas Streicher [this message]
[not found] ` <CAMH9A7ni+vD17O_NzuUDJjVcW90=7QeXDM3y27VPTGmtbwwH8Q@mail.gmail.com>
2024-01-23 3:11 ` Sorry Dusko Pavlovic
2024-01-23 10:12 ` small global sections vs definability of 1 Thomas Streicher
2024-02-08 12:51 ` Dusko Pavlovic
2024-02-08 16:36 ` **EXTERN** " streicher
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