Theorems · Theorem · category theory

CategoryTheory.GrothendieckTopology.Point.toPresheafFiberMap_w_assoc

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {D : Type u'} [inst_1 : CategoryTheory.Category.{v', u'} D]
  {J : CategoryTheory.GrothendieckTopology C} (Φ : J.Point) (F : CategoryTheory.Functor C D)
  (K : CategoryTheory.GrothendieckTopology D) [inst_2 : F.IsCocontinuous J K]
  [inst_3 : CategoryTheory.LocallySmall.{w, v', u'} D] {A : Type u''} [inst_4 : CategoryTheory.Category.{v'', u''} A]
  [inst_5 : CategoryTheory.Limits.HasColimitsOfSize.{w, w, v'', u''} A] {X Y : C} (f : X ⟶ Y) (x : Φ.fiber.obj X)
  (P : CategoryTheory.Functor Dᵒᵖ A) {Z : A} (h : (Φ.map F K).presheafFiber.obj P ⟶ Z),
  CategoryTheory.CategoryStruct.comp (P.map (F.map f).op)
      (CategoryTheory.CategoryStruct.comp (Φ.toPresheafFiberMap F K P X x) h) =
    CategoryTheory.CategoryStruct.comp
      (Φ.toPresheafFiberMap F K P Y ((CategoryTheory.ConcreteCategory.hom (Φ.fiber.map f)) x)) h

Defined in

Mathlib.CategoryTheory.Sites.Point.Map

Cited by

0 results in Mathlib

Foundations

Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Functor.IsCocontinuousCategoryTheory.LocallySmallCategoryTheory.CategoryCategoryTheory.Limits.HasColimitsOfSize