Theorems · Theorem · category theory

CategoryTheory.Functor.IsCoverDense.sheafHom_restrict_eq

∀ {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] {K : CategoryTheory.GrothendieckTopology D} {A : Type u_4}
  [inst_2 : CategoryTheory.Category.{v_4, u_4} A] {G : CategoryTheory.Functor C D} [inst_3 : G.IsCoverDense K]
  [inst_4 : G.IsLocallyFull K] {ℱ : CategoryTheory.Functor Dᵒᵖ A} {ℱ' : CategoryTheory.Sheaf K A}
  (α : G.op.comp ℱ ⟶ G.op.comp ℱ'.obj), G.op.whiskerLeft (CategoryTheory.Functor.IsCoverDense.sheafHom α) = α

The constructed sheafHom α is equal to α when restricted onto C.

Defined in

Mathlib.CategoryTheory.Sites.DenseSubsite.Basic

Cited by

0 results in Mathlib

Foundations

Depth 50 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Functor.IsCoverDenseCategoryTheory.Functor.IsLocallyFull