A map between two dagger categories that preserves the dagger category structure.
Definition
Definition
Given two -categories and , a -functor consists of a function with a function for every object , where is generally also denoted as , such that
for every object , ,
for every object and morphisms and ,
for every object and morphism , .
There is another definition which violates the principle of equivalence, since the definition of the dagger in a dagger category in this case is a functor that imposes equations on objects: A -functor between two -categories and is a functor of the underlying categories, which commutes with the -structures in that .