Theorems · Theorem · category theory

CategoryTheory.Functor.IsDenseSubsite.mapPreimage_comp_assoc

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] {D : Type u_2}
  [inst_1 : CategoryTheory.Category.{v_2, u_2} D] {J : CategoryTheory.GrothendieckTopology C}
  (K : CategoryTheory.GrothendieckTopology D) (G : CategoryTheory.Functor C D) {A : Type u_4}
  [inst_2 : CategoryTheory.Category.{v_4, u_4} A] [inst_3 : CategoryTheory.Functor.IsDenseSubsite J K G]
  (F : CategoryTheory.Sheaf J A) {X Y Z : C} (f : G.obj X ⟶ G.obj Y) (g : G.obj Y ⟶ G.obj Z) {Z_1 : A}
  (h : F.obj.obj (Opposite.op X) ⟶ Z_1),
  CategoryTheory.CategoryStruct.comp
      (CategoryTheory.Functor.IsDenseSubsite.mapPreimage K G F (CategoryTheory.CategoryStruct.comp f g)) h =
    CategoryTheory.CategoryStruct.comp (CategoryTheory.Functor.IsDenseSubsite.mapPreimage K G F g)
      (CategoryTheory.CategoryStruct.comp (CategoryTheory.Functor.IsDenseSubsite.mapPreimage K G F f) h)

Defined in

Mathlib.CategoryTheory.Sites.DenseSubsite.Basic

Cited by

0 results in Mathlib

Foundations

Depth 44 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Functor.IsDenseSubsite