nLab
epi-pullback

Definition

In a category a commutative square

q a b c\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 qa× cbq\to a\times_c b is an epimorphism. The object qq is then called an epi-pullback or quasi-pullback of the span bcab\to c\leftarrow a.

Remark

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

category: category theory

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