Theorems · Theorem · category theory

CategoryTheory.GrothendieckTopology.Point.skyscraperPresheafHomEquiv_naturality_right

∀ {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.HasProducts A]
  {P : CategoryTheory.Functor Cᵒᵖ A} {M N : A} [inst_3 : CategoryTheory.Limits.HasColimitsOfSize.{w, w, v', u'} A]
  (f : Φ.presheafFiber.obj P ⟶ M) (g : M ⟶ N),
  Φ.skyscraperPresheafHomEquiv (CategoryTheory.CategoryStruct.comp f g) =
    CategoryTheory.CategoryStruct.comp (Φ.skyscraperPresheafHomEquiv f) (Φ.skyscraperPresheafFunctor.map g)

Defined in

Mathlib.CategoryTheory.Sites.Point.Skyscraper

Cited by

3 results in Mathlib

Foundations

Depth 57 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasProductsCategoryTheory.Limits.HasColimitsOfSize