Theorems · Theorem · category theory

CategoryTheory.Presieve.shrinkFunctorHomEquiv_apply_coe

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {X : C} {S : CategoryTheory.Sieve X}
  [inst_1 : CategoryTheory.LocallySmall.{w, v₁, u₁} C] {F : CategoryTheory.Functor Cᵒᵖ (Type w)}
  (t : (CategoryTheory.Sieve.shrinkFunctor.{w, v₁, u₁} S).toFunctor ⟶ F) (Y : C) (f : Y ⟶ X) (hf : S.arrows f),
  ↑(CategoryTheory.Presieve.shrinkFunctorHomEquiv t) f hf =
    (CategoryTheory.ConcreteCategory.hom (t.app (Opposite.op Y))) ⟨CategoryTheory.shrinkYonedaObjObjEquiv.symm f, ⋯⟩

Defined in

Mathlib.CategoryTheory.Sites.IsSheafFor

Cited by

0 results in Mathlib

Foundations

Depth 34 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.LocallySmall