Theorems · Definition · category theory

CategoryTheory.MonoidalCategory.DayConvolution.isPointwiseLeftKanExtensionUnit

{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) →
              [self : CategoryTheory.MonoidalCategory.DayConvolution F G] →
                (CategoryTheory.Functor.LeftExtension.mk
                    (CategoryTheory.MonoidalCategory.DayConvolution.convolution F G)
                    (CategoryTheory.MonoidalCategory.DayConvolution.unit F G)).IsPointwiseLeftKanExtension

The transformation unit exhibits F ⊛ G as a pointwise left Kan extension of F ⊠ G along tensor C.

Defined in

Mathlib.CategoryTheory.Monoidal.DayConvolution

Cited by

2 results in Mathlib

Foundations

Depth 36 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.MonoidalCategory.DayConvolution