Theorems · Definition · category theory

CategoryTheory.MonoidalCategory.DayConvolutionInternalHom.isLimitWedge

{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] →
            [inst_4 : CategoryTheory.MonoidalClosed V] →
              {F G H : CategoryTheory.Functor C V} →
                (self : CategoryTheory.MonoidalCategory.DayConvolutionInternalHom F G H) →
                  (c : C) → CategoryTheory.Limits.IsLimit (CategoryTheory.Limits.Wedge.mk (H.obj c) (self.π c) ⋯)

The wedge defined by π and hπ is a limit wedge, i.e H.obj c is an end of internalHomDiagramFunctor F G|>.obj c.

Defined in

Mathlib.CategoryTheory.Monoidal.DayConvolution.Closed

Cited by

4 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.MonoidalCategoryCategoryTheory.MonoidalClosed