From: "Eduardo J. Dubuc" <edubuc@dm.uba.ar>
To: Thomas Streicher <streicher@mathematik.tu-darmstadt.de>
Cc: categories@mta.ca
Subject: Re: cleavages and choice
Date: Sun, 03 Aug 2014 17:41:59 -0300 [thread overview]
Message-ID: <E1XEHiG-0002rz-QU@mlist.mta.ca> (raw)
In-Reply-To: <E1XDwNF-0006oq-Mt@mlist.mta.ca>
On 03/08/14 06:22, Thomas Streicher wrote:
> One should not require all fibrations to be endowed with a cleavage. Rather
> one should be open to accept some strong choice principles on the meta level
> which allow one to assume the existence of cleavages whenever convenient.
> But, definitely, one should give most definitions and constructions in a way
> not referring to cleavages.
I completely agree with this, it is my own feeling beautifully and
synthetically expressed. I only add:
"... most definitions and constructions AND proofs in a way ..."
Also, that many times the use of cleavages may seem convenient, when in
fact it is not.
And I also put in the same bag the equivalences (which in general have
only one direction. Then one should proceed using the fully-faithfulness
and essentially surjectiveness whenever possible, and be free to assume
the existence of quasi-inverses only if it is necessary.
[For admin and other information see: http://www.mta.ca/~cat-dist/ ]
prev parent reply other threads:[~2014-08-03 20:41 UTC|newest]
Thread overview: 19+ messages / expand[flat|nested] mbox.gz Atom feed top
2014-07-20 16:18 Composition of Fibrations Jean Bénabou
2014-07-21 12:30 ` Steve Vickers
[not found] ` <3E52EFB7-7955-47B1-9B00-9F6F6152BBC1@cs.bham.ac.uk>
2014-07-21 18:02 ` Jean Bénabou
[not found] ` <32AB43B0-58DA-4375-A4FD-6C84F4E527EA@wanadoo.fr>
2014-07-21 20:06 ` Steve Vickers
[not found] ` <6EFFC44F-E933-412B-89F2-C33B598D78B0@cs.bham.ac.uk>
2014-07-22 4:24 ` Jean Bénabou
[not found] ` <9747FDFD-FF71-4ACE-8DD3-538462A1B283@wanadoo.fr>
2014-07-22 14:55 ` Steve Vickers
[not found] ` <C1C93FE1-09FF-43C4-A6DA-D0883440A2FC@cs.bham.ac.uk>
2014-07-22 21:52 ` Ross Street
2014-07-22 23:25 ` Eduardo J. Dubuc
2014-07-30 15:06 ` cleavages and choice Thomas Streicher
[not found] ` <20140730150643.GC19613@mathematik.tu-darmstadt.de>
2014-07-30 17:56 ` Jean Bénabou
2014-08-01 16:47 ` Eduardo J. Dubuc
2014-08-02 10:58 ` Marco Grandis
2014-08-03 15:17 ` Paul Levy
2014-08-03 16:30 ` Toby Bartels
2014-08-04 14:47 ` Marco Grandis
[not found] ` <82157841-9DE2-4D99-8533-57AAB99CD236@dima.unige.it>
2014-08-02 15:24 ` Eduardo J. Dubuc
[not found] ` <53DBC493.5060700@dm.uba.ar>
2014-08-01 17:52 ` Jean Bénabou
2014-08-03 9:22 ` Thomas Streicher
2014-08-03 20:41 ` Eduardo J. Dubuc [this message]
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