Theorems · Theorem · category theory

CategoryTheory.Equivalence.sheafCongr.inverse_obj_obj_obj

∀ {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 K A) (X_1 : Cᵒᵖ),
  ((CategoryTheory.Equivalence.sheafCongr.inverse J K e A).obj X).obj.obj X_1 =
    X.obj.obj (Opposite.op (e.functor.obj (Opposite.unop X_1)))

Defined in

Mathlib.CategoryTheory.Sites.Equivalence

Cited by

0 results in Mathlib

Foundations

Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Functor.IsDenseSubsite