Theorems · Theorem · category theory

CategoryTheory.GrothendieckTopology.Point.presheafFiber_hom_ext_iff

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {J : CategoryTheory.GrothendieckTopology C} {Φ : J.Point}
  {A : Type u'} [inst_1 : CategoryTheory.Category.{v', u'} A]
  [inst_2 : CategoryTheory.Limits.HasColimitsOfSize.{w, w, v', u'} A] {P : CategoryTheory.Functor Cᵒᵖ A} {T : A}
  {f g : Φ.presheafFiber.obj P ⟶ T},
  f = g ↔
    ∀ (X : C) (x : Φ.fiber.obj X),
      CategoryTheory.CategoryStruct.comp (Φ.toPresheafFiber X x P) f =
        CategoryTheory.CategoryStruct.comp (Φ.toPresheafFiber X x P) g

Defined in

Mathlib.CategoryTheory.Sites.Point.Basic

Cited by

0 results in Mathlib

Foundations

Depth 52 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasColimitsOfSize