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Theorems · Definition · category theory

CategoryTheory.MonoidalCategory.DayConvolution.unit

{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.MonoidalCategory.externalProduct F G ⟶
                  (CategoryTheory.MonoidalCategory.tensor C).comp
                    (CategoryTheory.MonoidalCategory.DayConvolution.convolution F G)

The chosen convolution between the functors.

Defined in
Mathlib.CategoryTheory.Monoidal.DayConvolution
Cited by
60 results in Mathlib
Foundations
Depth 35 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.MonoidalCategory.DayConvolution

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

CategoryTheory.MonoidalCategory.DayConvolution.map · cited by 21DayConvolution.mapCategoryTheory.MonoidalCategory.DayConvolution.unit_app_map_app_assoc · cited by 12DayConvolution.unit_app_m…CategoryTheory.MonoidalCategory.DayConvolution.corepresentableBy · cited by 10DayConvolution.corepresen…CategoryTheory.MonoidalCategory.DayConvolution.unit_app_map_app · cited by 6DayConvolution.unit_app_m…CategoryTheory.MonoidalCategory.DayConvolution.corepresentableBy₂' · cited by 5DayConvolution.corepresen…CategoryTheory.MonoidalCategory.DayConvolution.unit_app_braiding_hom_app · cited by 5DayConvolution.unit_app_b…CategoryTheory.MonoidalCategory.DayConvolution.unit_app_braiding_hom_app_assoc · cited by 5DayConvolution.unit_app_b…CategoryTheory.MonoidalCategory.DayConvolutionInternalHom.coev_app · cited by 5DayConvolutionInternalHom…CategoryTheory.MonoidalCategory.DayConvolution.associator_hom_unit_unit · cited by 4DayConvolution.associator…CategoryTheory.MonoidalCategory.DayConvolution.associator_hom_unit_unit_assoc · cited by 4DayConvolution.associator…CategoryTheory.MonoidalCategory.DayConvolution.uniqueUpToIso · cited by 4DayConvolution.uniqueUpTo…CategoryTheory.MonoidalCategory.DayConvolution.whiskerLeft_comp_unit_app_assoc · cited by 4DayConvolution.whiskerLef…CategoryTheory.MonoidalCategory.DayConvolutionInternalHom.unit_app_ev_app_app · cited by 4DayConvolutionInternalHom…CategoryTheory.MonoidalCategory.DayConvolutionUnit.leftUnitor_hom_unit_app · cited by 4DayConvolutionUnit.leftUn…CategoryTheory.MonoidalCategory.DayConvolutionUnit.rightUnitor_hom_unit_app · cited by 4DayConvolutionUnit.rightU…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.Functor · cited by 16252CategoryTheory.FunctorCategoryTheory.Functor.comp · cited by 6529Functor.compCategoryTheory.MonoidalCategory · cited by 3095CategoryTheory.MonoidalCa…CategoryTheory.MonoidalCategory.tensor · cited by 91MonoidalCategory.tensorCategoryTheory.MonoidalCategory.externalProduct · cited by 77MonoidalCategory.external…CategoryTheory.MonoidalCategory.DayConvolution.convolution · cited by 67DayConvolution.convolutionCategoryTheory.MonoidalCategory.DayConvolution · cited by 62MonoidalCategory.DayConvo…DayConvolution.unitCITED BYCITES

Cites9

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Cited by78

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