With braiding With duals for objects category with duals (list of them) dualizable object (what they have) ribbon category, a.k.a. tortile category With duals for morphisms With traces Closed structure Special sorts of products Semisimplicity Morphisms Internal monoids Examples Theorems In higher category theory In the strict sense of the word, a cartesian product is a product in Set, the category of sets. Hence for and two sets, their cartesian product is the set denoted whose elements are...