# nLab epi-pullback

###### Definition

In a category a commutative square

$\array{q&\to &a\\\downarrow&&\downarrow\\b&\to &c}$

is called an epi-pullback- or quasi-pullback- or epi cartesian-square if the induced morphism $q\to a\times_c b$ is an epimorphism. The object $q$ is then called an epi-pullback or quasi-pullback of the span $b\to c\leftarrow a$.

###### Remark

For a topos $T$ and $T^I$ its arrow category which is a topos, epi-pullback squares (in $T$) form a class of open maps? in $T^I$.

category: category theory

Created on March 9, 2012 19:00:14 by Stephan Alexander Spahn (79.219.113.208)