Group actions/representations: Every group "G" can be considered as a category with a single object whose morphisms are the elements of "G". A functor from "G" to Set is then nothing but a group action of "G" on a particular set, i.e. a "G"-set. Likewise, a functor from "G" to the category of vector spaces, Vect"K", is a linear representation of "G". In general, a functor can be considered as an "action" of "G" on an object in the category "C". If "C" is a group, then this action is a group homomorphism.