Theorems · Theorem · category theory

CategoryTheory.GrothendieckTopology.Point.toPresheafFiber_naturality_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.HasColimitsOfSize.{w, w, v', u'} A] {P Q : CategoryTheory.Functor Cᵒᵖ A} (g : P ⟶ Q)
  (X : C) (x : Φ.fiber.obj X) {F : A → A → Type uF} {carrier : A → Type w_1}
  {instFunLike : (X Y : A) → FunLike (F X Y) (carrier X) (carrier Y)} [inst_3 : CategoryTheory.ConcreteCategory A F]
  (x_1 : carrier (P.obj (Opposite.op X))),
  (CategoryTheory.ConcreteCategory.hom (Φ.presheafFiber.map g))
      ((CategoryTheory.ConcreteCategory.hom (Φ.toPresheafFiber X x P)) x_1) =
    (CategoryTheory.ConcreteCategory.hom (Φ.toPresheafFiber X x Q))
      ((CategoryTheory.ConcreteCategory.hom (g.app (Opposite.op X))) x_1)

Defined in

Mathlib.CategoryTheory.Sites.Point.Basic

Cited by

3 results in Mathlib

Foundations

Depth 54 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasColimitsOfSizeCategoryTheory.ConcreteCategory