Theorems · Theorem · category theory

CategoryTheory.GrothendieckTopology.whiskerRight_toPlus_comp_plusCompIso_hom_assoc

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] (J : CategoryTheory.GrothendieckTopology C) {D : Type u_1}
  [inst_1 : CategoryTheory.Category.{v_1, u_1} D] {E : Type u_2} [inst_2 : CategoryTheory.Category.{v_2, u_2} E]
  (F : CategoryTheory.Functor D E)
  [inst_3 :
    ∀ (J : CategoryTheory.Limits.MulticospanShape),
      CategoryTheory.Limits.HasLimitsOfShape (CategoryTheory.Limits.WalkingMulticospan J) D]
  [inst_4 :
    ∀ (J : CategoryTheory.Limits.MulticospanShape),
      CategoryTheory.Limits.HasLimitsOfShape (CategoryTheory.Limits.WalkingMulticospan J) E]
  [inst_5 :
    ∀ (X : C) (W : J.Cover X) (P : CategoryTheory.Functor Cᵒᵖ D),
      CategoryTheory.Limits.PreservesLimit (W.index P).multicospan F]
  (P : CategoryTheory.Functor Cᵒᵖ D) [inst_6 : ∀ (X : C), CategoryTheory.Limits.HasColimitsOfShape (J.Cover X)ᵒᵖ D]
  [inst_7 : ∀ (X : C), CategoryTheory.Limits.HasColimitsOfShape (J.Cover X)ᵒᵖ E]
  [inst_8 : ∀ (X : C), CategoryTheory.Limits.PreservesColimitsOfShape (J.Cover X)ᵒᵖ F]
  {Z : CategoryTheory.Functor Cᵒᵖ E} (h : J.plusObj (P.comp F) ⟶ Z),
  CategoryTheory.CategoryStruct.comp (CategoryTheory.Functor.whiskerRight (J.toPlus P) F)
      (CategoryTheory.CategoryStruct.comp (J.plusCompIso F P).hom h) =
    CategoryTheory.CategoryStruct.comp (J.toPlus (P.comp F)) h

Defined in

Mathlib.CategoryTheory.Sites.CompatiblePlus

Cited by

0 results in Mathlib

Foundations

Depth 52 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasLimitsOfShapeCategoryTheory.Limits.HasLimitsOfShapeCategoryTheory.Limits.PreservesLimitCategoryTheory.Limits.HasColimitsOfShapeCategoryTheory.Limits.HasColimitsOfShapeCategoryTheory.Limits.PreservesColimitsOfShape