Theorems · Definition · category theory

CategoryTheory.MonoidalCategory.DayConvolution.corepresentableBy

{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] →
                (((CategoryTheory.Functor.whiskeringLeft (C × C) C V).obj
                          (CategoryTheory.MonoidalCategory.tensor C)).comp
                      (CategoryTheory.coyoneda.obj
                        (Opposite.op (CategoryTheory.MonoidalCategory.externalProduct F G)))).CorepresentableBy
                  (CategoryTheory.MonoidalCategory.DayConvolution.convolution F G)

The universal property of left Kan extensions characterizes the functor corepresented by F ⊛ G.

Defined in

Mathlib.CategoryTheory.Monoidal.DayConvolution

Cited by

10 results in Mathlib

Foundations

Depth 40 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.MonoidalCategoryCategoryTheory.MonoidalCategory.DayConvolution