Cartesian morphism
From Wikipedia, the free encyclopedia
In mathematics, in particular in category theory, given a functor
- p : E → B
from a category E to a category B, a morphism
- f : X → Y
in E is cartesian (with respect to p) when for each object Z of E and each morphism
- w : pZ → pX
in B, the function
- f · — : Ew(Z, X) → Epf · w(Z,Y)
taking g to f · g is an isomorphism.
More explicitly, f is cartesian when for every morphism g : Z → Y in E such that pg = pf · w for some morphism w : pZ → pX in B, there exists a unique morphism h : Z → X in E above w (i.e. ph = w) with f · h = g.
