Theorems · Definition · category theory

CategoryTheory.MonoidalCategory.DayConvolutionUnit.isPointwiseLeftKanExtensionCan

{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 : CategoryTheory.Functor C V} →
              [self : CategoryTheory.MonoidalCategory.DayConvolutionUnit F] →
                (CategoryTheory.Functor.LeftExtension.mk F
                    { app := fun x => CategoryTheory.MonoidalCategory.DayConvolutionUnit.can,
                      naturality := ⋯ }).IsPointwiseLeftKanExtension

The canonical map 𝟙_ V ⟶ F.obj (𝟙_ C) exhibits F as a pointwise left Kan extension of fromPUnit.{0} 𝟙_ V along fromPUnit.{0} 𝟙_ C.

Defined in

Mathlib.CategoryTheory.Monoidal.DayConvolution

Cited by

2 results in Mathlib

Foundations

Depth 32 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.MonoidalCategory.DayConvolutionUnit