Theorems · Theorem · category theory

CategoryTheory.Presheaf.equalizerSieve_eq_top_iff

∀ {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)), CategoryTheory.Presheaf.equalizerSieve x y = ⊤ ↔ x = y

Defined in

Mathlib.CategoryTheory.Sites.LocallyInjective

Cited by

0 results in Mathlib

Foundations

Depth 28 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryFunLikeCategoryTheory.ConcreteCategory