Theorems · Inductive type · category theory

CategoryTheory.MonoidalCategory.DayConvolution

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    {V : Type u₂} →
      [inst_1 : CategoryTheory.Category.{v₂, u₂} V] →
        [CategoryTheory.MonoidalCategory C] →
          [CategoryTheory.MonoidalCategory V] →
            CategoryTheory.Functor C V → CategoryTheory.Functor C V → Type (max (max (max u₁ u₂) v₁) v₂)

A DayConvolution structure on functors F G : C ⥤ V is the data of a functor F ⊛ G : C ⥤ V, along with a unit F ⊠ G ⟶ tensor C ⋙ F ⊛ G that exhibits this functor as a pointwise left Kan extension of F ⊠ G along tensor C. This is a class used to prove various properties of such extensions, but registering global instances of this class is probably a bad idea.

Defined in

Mathlib.CategoryTheory.Monoidal.DayConvolution

Cited by

62 results in Mathlib

Foundations

Depth 2 from the axioms · uses no axioms

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.MonoidalCategory