| A polyad is a lax functor from a small category to the bicategory of categories, and a Hopf polyad is a comonoidal polyad whose fusion operators are invertible. |
| In contrast with previous works, the current study is based on phonological and functor innovations. |
| In fact, essentially every invariant studied by topologists can be made into a representable or corepresentable functor. |
| Also, objects that are not isomorphic in one category might become isomorphic when a functor is applied. |
| A new semisymmetrization functor, which maps the category of quasigroups with homotopies to the category of semisymmetric quasigroups with homomorphisms is given. |
| In this, as in some other articles the operation of modelling is represented as a functor in the categorical language. |
