Theorems · Theorem · category theory

CategoryTheory.GrothendieckTopology.Point.skyscraperSheafAdjunction_homEquiv_apply_hom

∀ {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]
  [inst_3 : CategoryTheory.Limits.HasColimitsOfSize.{w, w, v', u'} A] {F : CategoryTheory.Sheaf J A} {M : A}
  (f : Φ.presheafFiber.obj F.obj ⟶ M),
  ((Φ.skyscraperSheafAdjunction.homEquiv F M) f).hom = Φ.skyscraperPresheafHomEquiv f

Defined in

Mathlib.CategoryTheory.Sites.Point.Skyscraper

Cited by

1 results in Mathlib

Foundations

Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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