Theorems · Definition · category theory

CategoryTheory.GrothendieckTopology.overMapPullbackCongr

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    (J : CategoryTheory.GrothendieckTopology C) →
      (A : Type u') →
        [inst_1 : CategoryTheory.Category.{v', u'} A] →
          {X Y : C} → {f g : X ⟶ Y} → f = g → (J.overMapPullback A f ≅ J.overMapPullback A g)

Two identical morphisms give isomorphic overMapPullback functors on sheaves.

Defined in

Mathlib.CategoryTheory.Sites.Over

Cited by

10 results in Mathlib

Foundations

Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Category