Theorems · Definition · category theory

CategoryTheory.MonoidalCategory.LawfulDayConvolutionMonoidalCategoryStruct.convolution

(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.MonoidalCategoryStruct D] →
                  [inst_6 : CategoryTheory.MonoidalCategory.LawfulDayConvolutionMonoidalCategoryStruct C V D] →
                    (d d' : D) →
                      CategoryTheory.MonoidalCategory.DayConvolution
                        ((CategoryTheory.MonoidalCategory.LawfulDayConvolutionMonoidalCategoryStruct.ι C V D).obj d)
                        ((CategoryTheory.MonoidalCategory.LawfulDayConvolutionMonoidalCategoryStruct.ι C V D).obj d')

In a LawfulDayConvolutionMonoidalCategoryStruct, ι.obj (d ⊗ d') is a Day convolution of (ι C V).obj d and (ι C V).d'.

Defined in

Mathlib.CategoryTheory.Monoidal.DayConvolution

Cited by

4 results in Mathlib

Foundations

Depth 37 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.MonoidalCategoryCategoryTheory.CategoryCategoryTheory.MonoidalCategoryStructCategoryTheory.MonoidalCategory.LawfulDayConvolutionMonoidalCategoryStruct