The monoidal category structure on R-algebras

@[reducible, inline]

noncomputable abbrev AlgebraCat.instMonoidalCategory.tensorObj {R : Type u} [CommRing R] (X Y : AlgebraCat R) : AlgebraCat R

Auxiliary definition used to fight a timeout when building AlgebraCat.instMonoidalCategory.

Equations

• AlgebraCat.instMonoidalCategory.tensorObj X Y = AlgebraCat.of R (TensorProduct R ↑X ↑Y)

@[simp]

theorem AlgebraCat.instMonoidalCategory.tensorObj_carrier {R : Type u} [CommRing R] (X Y : AlgebraCat R) : ↑(AlgebraCat.instMonoidalCategory.tensorObj X Y) = TensorProduct R ↑X ↑Y

@[reducible, inline]

noncomputable abbrev AlgebraCat.instMonoidalCategory.tensorHom {R : Type u} [CommRing R] {W X Y Z : AlgebraCat R} (f : W ⟶ X) (g : Y ⟶ Z) : AlgebraCat.instMonoidalCategory.tensorObj W Y ⟶ AlgebraCat.instMonoidalCategory.tensorObj X Z

Auxiliary definition used to fight a timeout when building AlgebraCat.instMonoidalCategory.

Equations

• AlgebraCat.instMonoidalCategory.tensorHom f g = AlgebraCat.ofHom (Algebra.TensorProduct.map f.hom g.hom)

instance AlgebraCat.instMonoidalCategoryStruct {R : Type u} [CommRing R] : CategoryTheory.MonoidalCategoryStruct (AlgebraCat R)

Equations

• One or more equations did not get rendered due to their size.

noncomputable instance AlgebraCat.instMonoidalCategory {R : Type u} [CommRing R] : CategoryTheory.MonoidalCategory (AlgebraCat R)

Equations

• One or more equations did not get rendered due to their size.