In Mac Lane's, Categories for the Working Mathematician, on p.15 ex.3c) it asks to interpret "functor" when F: (group G)-->Set is a permutation representation of G.
Here is where I get stuck, G is one object category, so G gets mapped to one specific set, lets call it A, in the category Set. And each arrow of G gets mapped to a function from A to A? These functions must be bijections, in fact permutations, but how do we show that?
The definition of a permutation representation of a group G is h(g)(a)=g*a for g in G, a in A, but I do not know how to make sense of this definition in this context. Thanks.