instMonoid — Mathlib

English

If C is monoidal and Preadditive, and P.IsMonoidal, then the full subcategory P.FullSubcategory carries a MonoidalPreadditive structure (via faithful inclusion).

Русский

Если C моноидальна и преддобавительна, и P.IsMonoidal, то полная подкатегория P.FullSubcategory наследует структуру MonoidalPreadditive через верную вложенность.

LaTeX

$$$[MonoidalPreadditive C] \\ [MonoidalLinear R C] : MonoidalPreadditive P.FullSubcategory$$$

Lean4

/-- The skeleton of a monoidal category can be viewed as a monoid, where the multiplication is given by
the tensor product, and satisfies the monoid axioms since it is a skeleton.
-/
noncomputable instance instMonoid : Monoid (Skeleton C) :=
  monoidOfSkeletalMonoidal (skeleton_isSkeleton _).skel

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