Theorems · Theorem · category theory

CategoryTheory.GrothendieckTopology.Point.toPresheafFiber_w

∀ {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.HasColimitsOfSize.{w, w, v', u'} A] {X Y : C} (f : X ⟶ Y) (x : Φ.fiber.obj X)
  (P : CategoryTheory.Functor Cᵒᵖ A),
  CategoryTheory.CategoryStruct.comp (P.map f.op) (Φ.toPresheafFiber X x P) =
    Φ.toPresheafFiber Y ((CategoryTheory.ConcreteCategory.hom (Φ.fiber.map f)) x) P

Defined in

Mathlib.CategoryTheory.Sites.Point.Basic

Cited by

3 results in Mathlib

Foundations

Depth 51 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasColimitsOfSize