id -package:invertible package:free-categories

the identity morphism

A monoidal category structure on the category of quivers. This consists of a product bifunctor, a unit object and structure morphisms, an invertible associator,

qassoc . qdisassoc = id

qdisassoc . qassoc = id

and invertible left and right unitors,

qintro1 . qelim1 = id

qelim1 . qintro1 = id

qintro2 . qelim2 = id

qelim2 . qintro2 = id

that satisfy the pentagon equation,

qbimap id qassoc . qassoc . qbimap qassoc id = qassoc . qassoc

and the triangle equation,

qbimap id qelim1 . qassoc = qbimap qelim2 id

Map each element of the structure to a Monoid, and combine the results.