* pullback into product
@ 2009-10-19 15:15 Michael Barr
0 siblings, 0 replies; 2+ messages in thread
From: Michael Barr @ 2009-10-19 15:15 UTC (permalink / raw)
To: Categories list
If A ---> B <--- C is a pair of maps with the same codomain, then,
assuming pullback and product both exist, the map A x_B C ---> A x C is an
extremal monic. It is slightly tricky to prove, but must be well known.
Can anyone give me a reference?
Michael
[For admin and other information see: http://www.mta.ca/~cat-dist/ ]
^ permalink raw reply [flat|nested] 2+ messages in thread
* Re: pullback into product
@ 2009-10-19 23:11 George Janelidze
0 siblings, 0 replies; 2+ messages in thread
From: George Janelidze @ 2009-10-19 23:11 UTC (permalink / raw)
To: Michael Barr, Categories list
I am not sure about the earliest references, but the standard ("non-tricky")
facts are:
1. A x_B C ---> A x C is a regular mono, namely the equalizer of the two
obvious morphisms A x C ---> B.
2. Every regular mono is extremal.
George
----- Original Message -----
From: "Michael Barr" <barr@math.mcgill.ca>
To: "Categories list" <categories@mta.ca>
Sent: Monday, October 19, 2009 5:15 PM
Subject: categories: pullback into product
> If A ---> B <--- C is a pair of maps with the same codomain, then,
> assuming pullback and product both exist, the map A x_B C ---> A x C is an
> extremal monic. It is slightly tricky to prove, but must be well known.
> Can anyone give me a reference?
>
> Michael
>
>
> [For admin and other information see: http://www.mta.ca/~cat-dist/ ]
[For admin and other information see: http://www.mta.ca/~cat-dist/ ]
^ permalink raw reply [flat|nested] 2+ messages in thread
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