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× cb is an epimorphism. The object q is then called an epi-pullback or quasi-pullback of the span bca.


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 (