In mathematics, in particular category theory, given a functor

p:E→C

from a category E to a category C, a morphism

f : X → Y

in E is cartesian (with respect to p) when for each object Z of E and each morphism

γ : pZ → pX

in C, the function

f · — : E_γ(Z, X) → E_{pf · γ}(Z,Y)

taking g to f · g is an isomorphism.