Basic Categorical Constructions
Let $\mathcal C$and $\mathcal D$ be categories.
Opposite Category
The opposite category $\mathcal C^{op}$ of $\mathcal C$ has the same objects and morphisms $f\colon Y \to X \in \mathrm{Hom}_{\mathcal C^{op}}(X,Y)$ formally switching domain and codomain.
TensorCategories.opposite_category — Functionopposite_category(C::Category)Construct the category $Cᵒᵖ$.
TensorCategories.opposite_object — Functionopposite_object(X::Object)Regard the object $X ∈ C$ as an object in $Cᵒᵖ$.
TensorCategories.opposite_morphism — Functionopposite_morphism(f::Morphism)Regard the morphism $f ∈ C$ as a morphism in $Cᵒᵖ$.
Product Categories
Given a family of categories $\mathcal C_1,...,\mathcal C_n$ we can form the product category $\mathcal C = \mathcal C_1 \times \cdots \times \mathcal C_n$. Objects and morphism are just families of objects and morphisms. Structures all categories have and are preserved by the product will be available.
TensorCategories.product_category — Functionproduct_category(C::Category...)Construct the product category
TensorCategories.product_object — Functionproduct_object(X::Object...)Construct the product in the product category
TensorCategories.product_morphism — Functionproduct_morphism(f::Morphism...)Construct the product morphism in the product category