* Pullbacks of a family of arrows
@ 2012-02-08 20:29 Ohad Kammar
2012-02-09 15:02 ` Robin Houston
0 siblings, 1 reply; 2+ messages in thread
From: Ohad Kammar @ 2012-02-08 20:29 UTC (permalink / raw)
To: Categories List
What is the standard name for the limit of the diagram consisting of a morphism
f : A --> C
and an I-indexed family of morphisms
g_i : B_i --> C
where I is a set?
This is a slight generalisation of pullbacks. I am really interested
in the terminology for the following notion:
A class of morphisms M is stable under such generalised pullbacks if,
for all such limiting cones
a : P --> A
b_i : P --> B_i
if g_i are all in M, then so is the morphism a : P --> A
(This is a slight generalisation of stability of M under pullbacks.)
Thanks,
Ohad.
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* Re: Pullbacks of a family of arrows
2012-02-08 20:29 Pullbacks of a family of arrows Ohad Kammar
@ 2012-02-09 15:02 ` Robin Houston
0 siblings, 0 replies; 2+ messages in thread
From: Robin Houston @ 2012-02-09 15:02 UTC (permalink / raw)
To: Ohad Kammar; +Cc: Categories List
Wide pullback or fibre product, I think.
Sent from my telephone
On 8 Feb 2012, at 20:29, Ohad Kammar <ohad.kammar@ed.ac.uk> wrote:
> What is the standard name for the limit of the diagram consisting of a morphism
> f : A --> C
> and an I-indexed family of morphisms
> g_i : B_i --> C
> where I is a set?
>
> This is a slight generalisation of pullbacks. I am really interested
> in the terminology for the following notion:
>
> A class of morphisms M is stable under such generalised pullbacks if,
> for all such limiting cones
> a : P --> A
> b_i : P --> B_i
> if g_i are all in M, then so is the morphism a : P --> A
>
> (This is a slight generalisation of stability of M under pullbacks.)
>
[For admin and other information see: http://www.mta.ca/~cat-dist/ ]
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