From: "Eduardo J. Dubuc" <edubuc@dm.uba.ar>
To: Marco Grandis <grandis@dima.unige.it>
Cc: categories@mta.ca
Subject: Re: cleavages and choice
Date: Sat, 02 Aug 2014 12:24:09 -0300 [thread overview]
Message-ID: <E1XDwM1-0006lm-U6@mlist.mta.ca> (raw)
In-Reply-To: <82157841-9DE2-4D99-8533-57AAB99CD236@dima.unige.it>
Dear Marco, supposing you are right (which is probably the case, I have
not examined closely the question of the monoidal structure of Ab or the
bicategory of spans), this does not contradicts my points. I never said
that choices should be banned, I said that they should not be used when
not necessary, because of plenty of different reasons.
best e.d.
On 02/08/14 07:58, Marco Grandis wrote:
> Dear Eduardo,
>
> I agree with many things in your message, but I think you are taking
> your argument too far. Talking of pullbacks you say:
>
>> We precisely teach in category theory courses that you should not
>> work with any particular choice between the choices.
>
> I agree that it is better to avoid such a choice when possible. Yet
> you cannot define a bicategory of spans without assuming that such a
> choice has been made; in the same way as you cannot define the (good)
> monoidal structure of Ab without recurring to a choice of tensor
> products. Such a situation, we all know, generally arises in
> non-strict bicategories (and monoidal categories, in particular).
>
> Unless you want to redefine bicategories replacing the composition of
> arrows with an existence property. I still prefer working with a
> choice (eg of pullbacks) to such a complicated structure.
>
> Best regards
>
> Marco
>
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next prev parent reply other threads:[~2014-08-02 15:24 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 [this message]
[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
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