Theorems · Theorem · category theory

CategoryTheory.GrothendieckTopology.overMapPullback_assoc_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 Z T : C} (f : X ⟶ Y) (g : Y ⟶ Z) (h : Z ⟶ T)
  {Z_1 : CategoryTheory.Functor (CategoryTheory.Sheaf (J.over T) A) (CategoryTheory.Sheaf (J.over X) A)}
  (h_1 : J.overMapPullback A (CategoryTheory.CategoryStruct.comp (CategoryTheory.CategoryStruct.comp f g) h) ⟶ Z_1),
  CategoryTheory.CategoryStruct.comp (J.overMapPullbackComp A f (CategoryTheory.CategoryStruct.comp g h)).inv
      (CategoryTheory.CategoryStruct.comp
        (CategoryTheory.Functor.whiskerRight (J.overMapPullbackComp A g h).inv (J.overMapPullback A f))
        (CategoryTheory.CategoryStruct.comp
          ((J.overMapPullback A h).associator (J.overMapPullback A g) (J.overMapPullback A f)).hom
          (CategoryTheory.CategoryStruct.comp ((J.overMapPullback A h).whiskerLeft (J.overMapPullbackComp A f g).hom)
            (CategoryTheory.CategoryStruct.comp (J.overMapPullbackComp A (CategoryTheory.CategoryStruct.comp f g) h).hom
              h_1)))) =
    CategoryTheory.CategoryStruct.comp (J.overMapPullbackCongr A ⋯).hom h_1

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