Theorems · Theorem · category theory

CategoryTheory.GrothendieckTopology.Point.Hom.presheafFiber_app

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {J : CategoryTheory.GrothendieckTopology C} {A : Type u'}
  [inst_1 : CategoryTheory.Category.{v', u'} A] [inst_2 : CategoryTheory.Limits.HasColimitsOfSize.{w, w, v', u'} A]
  {Φ₁ Φ₂ : J.Point} (f : Φ₁ ⟶ Φ₂) (P : CategoryTheory.Functor Cᵒᵖ A),
  (CategoryTheory.GrothendieckTopology.Point.Hom.presheafFiber f).app P =
    Φ₂.presheafFiberDesc (fun X x => Φ₁.toPresheafFiber X ((CategoryTheory.ConcreteCategory.hom (f.hom.app X)) x) P) ⋯

Defined in

Mathlib.CategoryTheory.Sites.Point.Category

Cited by

3 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasColimitsOfSize