Theorems · Definition · category theory

CategoryTheory.MonoidalCategory.DayConvolution.associator

{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] →
            (F G : CategoryTheory.Functor C V) →
              [inst_4 : CategoryTheory.MonoidalCategory.DayConvolution F G] →
                (H : CategoryTheory.Functor C V) →
                  [inst_5 : CategoryTheory.MonoidalCategory.DayConvolution G H] →
                    [inst_6 :
                        CategoryTheory.MonoidalCategory.DayConvolution F
                          (CategoryTheory.MonoidalCategory.DayConvolution.convolution G H)] →
                      [inst_7 :
                          CategoryTheory.MonoidalCategory.DayConvolution
                            (CategoryTheory.MonoidalCategory.DayConvolution.convolution F G) H] →
                        [∀ (v : V) (d : C),
                              CategoryTheory.Limits.PreservesColimitsOfShape
                                (CategoryTheory.CostructuredArrow (CategoryTheory.MonoidalCategory.tensor C) d)
                                (CategoryTheory.MonoidalCategory.tensorLeft v)] →
                          [∀ (v : V) (d : C),
                                CategoryTheory.Limits.PreservesColimitsOfShape
                                  (CategoryTheory.CostructuredArrow (CategoryTheory.MonoidalCategory.tensor C) d)
                                  (CategoryTheory.MonoidalCategory.tensorRight v)] →
                            CategoryTheory.MonoidalCategory.DayConvolution.convolution
                                (CategoryTheory.MonoidalCategory.DayConvolution.convolution F G) H ≅
                              CategoryTheory.MonoidalCategory.DayConvolution.convolution F
                                (CategoryTheory.MonoidalCategory.DayConvolution.convolution G H)

The associator isomorphism for Day convolution

Defined in

Mathlib.CategoryTheory.Monoidal.DayConvolution

Cited by

11 results in Mathlib

Foundations

Depth 56 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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