Theorems · Definition · category theory

CategoryTheory.MonoidalCategory.LawfulDayConvolutionMonoidalCategoryStruct.convolutionExtensionUnit

(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} →
                  [self : CategoryTheory.MonoidalCategory.LawfulDayConvolutionMonoidalCategoryStruct C V D] →
                    (d d' : D) →
                      CategoryTheory.MonoidalCategory.externalProduct
                          ((CategoryTheory.MonoidalCategory.LawfulDayConvolutionMonoidalCategoryStruct.ι C V D).obj d)
                          ((CategoryTheory.MonoidalCategory.LawfulDayConvolutionMonoidalCategoryStruct.ι C V D).obj
                            d') ⟶
                        (CategoryTheory.MonoidalCategory.tensor C).comp
                          ((CategoryTheory.MonoidalCategory.LawfulDayConvolutionMonoidalCategoryStruct.ι C V D).obj
                            (CategoryTheory.MonoidalCategoryStruct.tensorObj d d'))

a natural transformation ι.obj d ⊠ ι.obj d' ⟶ tensor C ⋙ ι.obj (d ⊗ d')

Defined in

Mathlib.CategoryTheory.Monoidal.DayConvolution

Cited by

8 results in Mathlib

Foundations

Depth 35 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.MonoidalCategory.LawfulDayConvolutionMonoidalCategoryStruct