Theorems · Theorem · category theory

CategoryTheory.GrothendieckTopology.plusCompIso_whiskerLeft

∀ {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]
  [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), CategoryTheory.Limits.HasColimitsOfShape (J.Cover X)ᵒᵖ D]
  [inst_6 : ∀ (X : C), CategoryTheory.Limits.HasColimitsOfShape (J.Cover X)ᵒᵖ E] {F G : CategoryTheory.Functor D E}
  (η : F ⟶ G) (P : CategoryTheory.Functor Cᵒᵖ D)
  [inst_7 : ∀ (X : C), CategoryTheory.Limits.PreservesColimitsOfShape (J.Cover X)ᵒᵖ F]
  [inst_8 :
    ∀ (X : C) (W : J.Cover X) (P : CategoryTheory.Functor Cᵒᵖ D),
      CategoryTheory.Limits.PreservesLimit (W.index P).multicospan F]
  [inst_9 : ∀ (X : C), CategoryTheory.Limits.PreservesColimitsOfShape (J.Cover X)ᵒᵖ G]
  [inst_10 :
    ∀ (X : C) (W : J.Cover X) (P : CategoryTheory.Functor Cᵒᵖ D),
      CategoryTheory.Limits.PreservesLimit (W.index P).multicospan G],
  CategoryTheory.CategoryStruct.comp ((J.plusObj P).whiskerLeft η) (J.plusCompIso G P).hom =
    CategoryTheory.CategoryStruct.comp (J.plusCompIso F P).hom (J.plusMap (P.whiskerLeft η))

Defined in

Mathlib.CategoryTheory.Sites.CompatiblePlus

Cited by

1 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.HasColimitsOfShapeCategoryTheory.Limits.HasColimitsOfShapeCategoryTheory.Limits.PreservesColimitsOfShapeCategoryTheory.Limits.PreservesLimitCategoryTheory.Limits.PreservesColimitsOfShapeCategoryTheory.Limits.PreservesLimit