Theorems · Theorem · category theory

CategoryTheory.GrothendieckTopology.Point.presheafFiberMap_hom_ext

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {D : Type u'} [inst_1 : CategoryTheory.Category.{v', u'} D]
  {J : CategoryTheory.GrothendieckTopology C} (Φ : J.Point) (F : CategoryTheory.Functor C D)
  (K : CategoryTheory.GrothendieckTopology D) [inst_2 : F.IsCocontinuous J K]
  [inst_3 : CategoryTheory.LocallySmall.{w, v', u'} D] {A : Type u''} [inst_4 : CategoryTheory.Category.{v'', u''} A]
  [inst_5 : CategoryTheory.Limits.HasColimitsOfSize.{w, w, v'', u''} A] {P : CategoryTheory.Functor Dᵒᵖ A} {T : A}
  {f g : (Φ.map F K).presheafFiber.obj P ⟶ T},
  (∀ (X : C) (x : Φ.fiber.obj X),
      CategoryTheory.CategoryStruct.comp (Φ.toPresheafFiberMap F K P X x) f =
        CategoryTheory.CategoryStruct.comp (Φ.toPresheafFiberMap F K P X x) g) →
    f = g

Defined in

Mathlib.CategoryTheory.Sites.Point.Map

Cited by

1 results in Mathlib

Foundations

Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Functor.IsCocontinuousCategoryTheory.LocallySmallCategoryTheory.CategoryCategoryTheory.Limits.HasColimitsOfSize