epi-pullback

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 $b\to c\leftarrow a$.

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 at 19:00:14. See the history of this page for a list of all contributions to it.