a monoidal category formula_1 is, loosely speaking, a category equipped with a notion resembling the tensor product (of vector spaces, say). that is, for any two objects formula_2, there is an object formula_3. the assignment formula_4 is supposed to be functorial and needs to require a number of further properties such as a unit object 1 and an associativity isomorphism. such a category is called braided if there are isomorphisms