Theorems · Theorem · category theory

CategoryTheory.MonoidalCategory.InducedLawfulDayConvolutionMonoidalCategoryStructCore.id_tensorHom

∀ (C : Type u₁) [inst : CategoryTheory.Category.{v₁, u₁} C] (V : Type u₂) [inst_1 : CategoryTheory.Category.{v₂, u₂} V]
  [inst_2 : CategoryTheory.MonoidalCategory C] [inst_3 : CategoryTheory.MonoidalCategory V] (D : Type u₃)
  [inst_4 : CategoryTheory.Category.{v₃, u₃} D]
  [inst_5 : CategoryTheory.MonoidalCategory.InducedLawfulDayConvolutionMonoidalCategoryStructCore C V D]
  [inst_6 :
    ∀ (v : V) (d : C),
      CategoryTheory.Limits.PreservesColimitsOfShape
        (CategoryTheory.CostructuredArrow (CategoryTheory.MonoidalCategory.tensor C) d)
        (CategoryTheory.MonoidalCategory.tensorLeft v)]
  [inst_7 :
    ∀ (v : V) (d : C),
      CategoryTheory.Limits.PreservesColimitsOfShape
        (CategoryTheory.CostructuredArrow (CategoryTheory.MonoidalCategory.tensor C) d)
        (CategoryTheory.MonoidalCategory.tensorRight v)]
  [inst_8 :
    ∀ (v : V) (d : C),
      CategoryTheory.Limits.PreservesColimitsOfShape
        (CategoryTheory.CostructuredArrow
          (CategoryTheory.Functor.fromPUnit (CategoryTheory.MonoidalCategoryStruct.tensorUnit C)) d)
        (CategoryTheory.MonoidalCategory.tensorRight v)]
  [inst_9 :
    ∀ (v : V) (d : C),
      CategoryTheory.Limits.PreservesColimitsOfShape
        (CategoryTheory.CostructuredArrow
          (CategoryTheory.Functor.fromPUnit (CategoryTheory.MonoidalCategoryStruct.tensorUnit C)) d)
        (CategoryTheory.MonoidalCategory.tensorLeft v)]
  (x : D) {y y' : D} (f : y ⟶ y'),
  CategoryTheory.MonoidalCategoryStruct.tensorHom (CategoryTheory.CategoryStruct.id x) f =
    CategoryTheory.MonoidalCategoryStruct.whiskerLeft x f

Defined in

Mathlib.CategoryTheory.Monoidal.DayConvolution

Cited by

0 results in Mathlib

Foundations

Depth 58 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.MonoidalCategoryCategoryTheory.CategoryCategoryTheory.MonoidalCategory.InducedLawfulDayConvolutionMonoidalCategoryStructCoreCategoryTheory.Limits.PreservesColimitsOfShapeCategoryTheory.Limits.PreservesColimitsOfShapeCategoryTheory.Limits.PreservesColimitsOfShapeCategoryTheory.Limits.PreservesColimitsOfShape