A monoidal dagger category is a dagger category with a dagger functor from the product dagger category of to itself called the tensor product and an object called the tensor unit, such that
for all morphisms and ,
for all objects , , , a natural unitary isomorphism? called the associator of , , and ,
for objects , a natural unitary isomorphism called the left unitor of ,
for objects , a natural unitary isomorphism called the right unitor of