Theorems · Theorem · category theory

CategoryTheory.GrothendieckTopology.Point.toPresheafFiber_naturality

∀ {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] {P Q : CategoryTheory.Functor Cᵒᵖ A} (g : P ⟶ Q)
  (X : C) (x : Φ.fiber.obj X),
  CategoryTheory.CategoryStruct.comp (Φ.toPresheafFiber X x P) (Φ.presheafFiber.map g) =
    CategoryTheory.CategoryStruct.comp (g.app (Opposite.op X)) (Φ.toPresheafFiber X x Q)

Defined in

Mathlib.CategoryTheory.Sites.Point.Basic

Cited by

3 results in Mathlib

Foundations

Depth 53 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasColimitsOfSize