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From: P.T.Johnstone@dpmms.cam.ac.uk
To: André <joyal.andre@uqam.ca>, categories@mta.ca
Subject: Re: Four problems
Date: 29 Apr 2010 11:16:54 +0100	[thread overview]
Message-ID: <E1O7qha-0006yv-8A@mailserv.mta.ca> (raw)
In-Reply-To: <E1O761X-0006lG-Lm@mailserv.mta.ca>

On Apr 28 2010, Joyal, André wrote:

>Jean Benabou has formulated four problems of category theory.
>They were communicated to a restricted list of peoples, not a private list.
>I see no serious raisons for not sharing these problems with everyones. 
>Here they are:
>
>
>>Prob1. What conditions must a (small)  category C satisfy in order that :
>>there exists a faithful functor  F: C --> G  where  G  is a groupoid?    
>>(Generalized "Mal'cev" conditions)
>
This problem is solved in a recent paper of mine "On embedding categories
in groupoids" in Math. Proc. Camb. Philos. Soc., vol. 145. Actually, the
problem was essentially solved by Mal'cev and (independently) by Jim Lambek,
who gave necessary and sufficient conditions for a semigroup to be
embeddable in a group; all one has to do is to observe that the same
conditions work in the situation when one has several objects.

Peter Johnstone

[For admin and other information see: http://www.mta.ca/~cat-dist/ ]


  reply	other threads:[~2010-04-29 10:16 UTC|newest]

Thread overview: 8+ messages / expand[flat|nested]  mbox.gz  Atom feed  top
2010-04-26 15:09 Joyal, André
2010-04-29 10:16 ` P.T.Johnstone [this message]
2010-05-01  1:13 ` tholen
     [not found] ` <20100430211359.nbm6pfhjk0wgkgwc@mail.math.yorku.ca>
2010-05-02  1:21   ` RE : categories: " Joyal, André
     [not found]   ` <B3C24EA955FF0C4EA14658997CD3E25E370F57B0@CAHIER.gst.uqam.ca>
     [not found]     ` <B3C24EA955FF0C4EA14658997CD3E25E370F57B1@CAHIER.gst.uqam.ca>
2010-05-02 13:58       ` Four problems corrected Joyal, André
     [not found] ` <B3C24EA955FF0C4EA14658997CD3E25E370F57B2@CAHIER.gst.uqam.ca>
2010-05-03  1:06   ` Four problems(corrected2) tholen
2010-05-03 22:36     ` Eduardo J. Dubuc
     [not found]     ` <B3C24EA955FF0C4EA14658997CD3E25E370F57B9@CAHIER.gst.uqam.ca>
2010-05-07 15:21       ` Re=3A_Four_problems=28corrected2=29?= Joyal, André

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