Theorems · Theorem · category theory

CategoryTheory.Equivalence.sheafCongr.functor_obj_obj_map

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] (J : CategoryTheory.GrothendieckTopology C) {D : Type u₂}
  [inst_1 : CategoryTheory.Category.{v₂, u₂} D] (K : CategoryTheory.GrothendieckTopology D) (e : C ≌ D) (A : Type u₃)
  [inst_2 : CategoryTheory.Category.{v₃, u₃} A] [inst_3 : CategoryTheory.Functor.IsDenseSubsite K J e.inverse]
  (X : CategoryTheory.Sheaf J A) {X_1 Y : Dᵒᵖ} (f : X_1 ⟶ Y),
  ((CategoryTheory.Equivalence.sheafCongr.functor J K e A).obj X).obj.map f = X.obj.map (e.inverse.map f.unop).op

Defined in

Mathlib.CategoryTheory.Sites.Equivalence

Cited by

0 results in Mathlib

Foundations

Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Functor.IsDenseSubsite