Theorems · Theorem · category theory

CategoryTheory.Functor.IsDenseSubsite.mapPreimage_comp

∀ {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),
  CategoryTheory.Functor.IsDenseSubsite.mapPreimage K G F (CategoryTheory.CategoryStruct.comp f g) =
    CategoryTheory.CategoryStruct.comp (CategoryTheory.Functor.IsDenseSubsite.mapPreimage K G F g)
      (CategoryTheory.Functor.IsDenseSubsite.mapPreimage K G F f)

Defined in

Mathlib.CategoryTheory.Sites.DenseSubsite.Basic

Cited by

4 results in Mathlib

Foundations

Depth 43 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Functor.IsDenseSubsite