nLab epi-pullback




In category theory, a commutative square

q a b c \array{ q & \longrightarrow & a \\ \big\downarrow && \big\downarrow \\ b & \longrightarrow & c }

in a category with finite limits is (sometimes) called an epi-pullback (or quasi-pullback or epi cartesian-square) if the canonical morphism qa× cbq\to a\times_c b to the fiber product (induced by its universal property) is an epimorphism.

Spcifically, the object qq is then called an epi-pullback or quasi-pullback of the span bcab\to c\leftarrow a.



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 morphisms in T IT^I.


Lax double functors Rel(A)Rel(B)Rel(A) \to Rel(B) are equivalent to functors ABA \to B preserving quasi-pullbacks.


  • Robert Paré, Some things about double categories, Talk at Virtual Double Categories Workshop 2022, pdf

Last revised on March 14, 2023 at 22:24:16. See the history of this page for a list of all contributions to it.