Theorems · Theorem · category theory

CategoryTheory.Presheaf.equalizerSieve_apply

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {D : Type u'} [inst_1 : CategoryTheory.Category.{v', u'} D]
  {FD : D → D → Type u_1} {CD : D → Type w} [inst_2 : (X Y : D) → FunLike (FD X Y) (CD X) (CD Y)]
  [inst_3 : CategoryTheory.ConcreteCategory D FD] {F : CategoryTheory.Functor Cᵒᵖ D} {X : Cᵒᵖ}
  (x y : CategoryTheory.ToType (F.obj X)) (x_1 : C) (f : x_1 ⟶ Opposite.unop X),
  (CategoryTheory.Presheaf.equalizerSieve x y).arrows f =
    ((CategoryTheory.ConcreteCategory.hom (F.map f.op)) x = (CategoryTheory.ConcreteCategory.hom (F.map f.op)) y)

Defined in

Mathlib.CategoryTheory.Sites.LocallyInjective

Cited by

6 results in Mathlib

Foundations

Depth 13 from the axioms · uses propext

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryFunLikeCategoryTheory.ConcreteCategory