Theorems · Theorem · category theory

CategoryTheory.GrothendieckTopology.Point.skyscraperPresheafHomEquiv_symm_apply

∀ {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 : A} [inst_3 : CategoryTheory.Limits.HasColimitsOfSize.{w, w, v', u'} A]
  (g : P ⟶ Φ.skyscraperPresheaf M),
  Φ.skyscraperPresheafHomEquiv.symm g =
    Φ.presheafFiberDesc
      (fun X x =>
        CategoryTheory.CategoryStruct.comp (g.app (Opposite.op X)) (CategoryTheory.Limits.Pi.π (fun t => M) x))
      ⋯

Defined in

Mathlib.CategoryTheory.Sites.Point.Skyscraper

Cited by

1 results in Mathlib

Foundations

Depth 55 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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