Re: Name for a concept

[Eduardo Dubuc <edubuc@dm.uba.ar>]

>
> 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.