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.
- Cited by
- 60 results in Mathlib
- Foundations
- Depth 35 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement and proof · cited by 32,673
- Quiver.Homstatement · cited by 32,603
- CategoryTheory.Functorstatement and proof · cited by 16,252
- CategoryTheory.Functor.compstatement · cited by 6,529
- CategoryTheory.MonoidalCategorystatement and proof · cited by 3,095
- CategoryTheory.MonoidalCategory.tensorstatement · cited by 91
- CategoryTheory.MonoidalCategory.externalProductstatement · cited by 77
- CategoryTheory.MonoidalCategory.DayConvolution.convolutionstatement · cited by 67
- CategoryTheory.MonoidalCategory.DayConvolutionstatement and proof · cited by 62
Cited by78
Results whose statement or proof uses this declaration.
- CategoryTheory.MonoidalCategory.DayConvolution.mapproof · cited by 21
- CategoryTheory.MonoidalCategory.DayConvolution.unit_app_map_app_assocstatement and proof · cited by 12
- CategoryTheory.MonoidalCategory.DayConvolution.corepresentableByproof · cited by 10
- CategoryTheory.MonoidalCategory.DayConvolution.unit_app_map_appstatement and proof · cited by 6
- CategoryTheory.MonoidalCategory.DayConvolution.corepresentableBy₂'proof · cited by 5
- CategoryTheory.MonoidalCategory.DayConvolution.unit_app_braiding_hom_appstatement and proof · cited by 5
- CategoryTheory.MonoidalCategory.DayConvolution.unit_app_braiding_hom_app_assocstatement and proof · cited by 5
- CategoryTheory.MonoidalCategory.DayConvolutionInternalHom.coev_appproof · cited by 5
- CategoryTheory.MonoidalCategory.DayConvolution.associator_hom_unit_unitstatement and proof · cited by 4
- CategoryTheory.MonoidalCategory.DayConvolution.associator_hom_unit_unit_assocstatement and proof · cited by 4
- CategoryTheory.MonoidalCategory.DayConvolution.uniqueUpToIsoproof · cited by 4
- CategoryTheory.MonoidalCategory.DayConvolution.whiskerLeft_comp_unit_app_assocstatement and proof · cited by 4