Theorems · Theorem · category theory

CategoryTheory.GrothendieckTopology.overMapPullback_comp_id_assoc

∀ {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 : X ⟶ Y)
  {Z : CategoryTheory.Functor (CategoryTheory.Sheaf (J.over Y) A) (CategoryTheory.Sheaf (J.over X) A)}
  (h : J.overMapPullback A f ⟶ Z),
  CategoryTheory.CategoryStruct.comp (J.overMapPullbackComp A f (CategoryTheory.CategoryStruct.id Y)).inv
      (CategoryTheory.CategoryStruct.comp
        (CategoryTheory.Functor.whiskerRight (J.overMapPullbackId A Y).hom (J.overMapPullback A f))
        (CategoryTheory.CategoryStruct.comp (J.overMapPullback A f).leftUnitor.hom h)) =
    CategoryTheory.CategoryStruct.comp (J.overMapPullbackCongr A ⋯).hom h

Defined in

Mathlib.CategoryTheory.Sites.Over

Cited by

0 results in Mathlib

Foundations

Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Category