English
Composition of η with tensorDesc validates the universal property of the Day convolution
Русский
Составление η с tensorDesc подтверждает универсальное свойство Day конволюции.
LaTeX
$$$ (\\eta F G).app (x,y) \\; \\circ \\; (tensorDesc α).natTrans.app (x ⊗ y) = α.app (x,y) $$$
Lean4
@[simps! ι_obj ι_map]
instance : LawfulDayConvolutionMonoidalCategoryStruct C V (C ⊛⥤ V) :=
lawfulDayConvolutionMonoidalCategoryStructOfHasDayConvolutions (equiv C V).functor (equiv C V).fullyFaithfulFunctor
(fun _ _ => ⟨_, ⟨equiv C V |>.counitIso.app _⟩⟩) ⟨_, ⟨equiv C V |>.counitIso.app _⟩⟩
