Theorems · Inductive type · category theory

CategoryTheory.MonoidalCategory.DayConvolutionInternalHom

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    {V : Type u₂} →
      [inst_1 : CategoryTheory.Category.{v₂, u₂} V] →
        [CategoryTheory.MonoidalCategory C] →
          [inst_3 : CategoryTheory.MonoidalCategory V] →
            [CategoryTheory.MonoidalClosed V] →
              CategoryTheory.Functor C V →
                CategoryTheory.Functor C V → CategoryTheory.Functor C V → Type (max (max (max u₁ u₂) v₁) v₂)

DayConvolutionInternalHom F G H asserts that H is the value at G of an internal hom functor of F for the Day convolution monoidal structure. This is phrased as the data of a limit CategoryTheory.Wedge (i.e an end) on internalHomDiagramFunctor F|>.obj G|>.obj c and c, with tip (H.obj G).obj c and a compatibility condition asserting that the functoriality of H identifies to the functoriality of ends.

Defined in

Mathlib.CategoryTheory.Monoidal.DayConvolution.Closed

Cited by

17 results in Mathlib

Foundations

Depth 3 from the axioms · uses no axioms

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.MonoidalCategoryCategoryTheory.MonoidalClosed