epi-pullback

In a category a commutative square

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

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 19:00:14
by Stephan Alexander Spahn
(79.219.113.208)