From: jean benabou <jean.benabou@wanadoo.fr>
To: Categories <categories@mta.ca>
Subject: Re: Name for a concept
Date: Tue, 6 Dec 2005 11:12:54 +0100 [thread overview]
Message-ID: <DD9C6EB0-6640-11DA-A9B5-000393B90F2C@wanadoo.fr> (raw)
Continuation of namings
(1) - Is there a standard name for the squares where the canonical map
is monic , i.e. the pair of maps A --->B and A --->C is jointly
monic. I propose semi-pullback
(2)- In most cases the canonical map being epic is not what one really
wants. Of course Joyal assumes the category where the maps live to be a
pre-topos, then it's enough, otherwise one cannot "compose" such
squares. Do we have to rename the squares where the canonical map is a
universal epi, or those where its a universal regular epi?
In view of (1), one would like to say that a square is a pullback iff
it is both a quasi and semi pullback
Début du message réexpédié :
> De: Eduardo Dubuc <edubuc@dm.uba.ar>
> Date: Lun 5 déc 2005 17:16:13 Europe/Paris
> À: categories@mta.ca (Categories list)
> Objet: categories: Re: Name for a concept
>
>>
>> Is there a standard name for a square
>> A ----> B
>> | |
>> | |
>> | |
>> v v
>> C ----> D
>> in which the canonical map A ---> B x_D C is epic?
>
>
> These are called "quasi-pullbacks" by Joyal, and they form a class of
> "open maps" in the category of squares. The pullbacks form the
> corresponding class of etal maps. These two classes are essential for
> the
> development of the theory (etal class and open class in the sense of
> Joyal). There are published articles by Joyal and Moerdijk on the
> subject.
>
>
>
>
>
next reply other threads:[~2005-12-06 10:12 UTC|newest]
Thread overview: 12+ messages / expand[flat|nested] mbox.gz Atom feed top
2005-12-06 10:12 jean benabou [this message]
2005-12-07 0:58 ` Toby Bartels
2005-12-07 19:15 ` Eduardo Dubuc
-- strict thread matches above, loose matches on Subject: below --
2005-12-08 11:26 name " Clemens.BERGER
2005-12-08 11:06 Clemens.BERGER
2005-12-07 13:36 Name " Peter Freyd
2005-12-05 14:44 Marco Grandis
2005-12-01 1:48 Michael Barr
2005-12-02 11:19 ` Ronald Brown
2005-12-02 13:51 ` Marco Grandis
2005-12-05 16:16 ` Eduardo Dubuc
2005-12-07 11:04 ` Marco Grandis
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