I don't know why just saying the following block of text combined with walking through a bunch of examples and how each of the examples fulfills those propertie

I don't know why just saying the following block of text combined with walking through a bunch of examples and how each of the examples fulfills those properties, wouldn't be sufficient : ' If F is a functor, then for any A,B,C,f,g, such that f : A -> B , and g : B -> C, (where we write composition with a semicolon so that the composition of f and g is written f;g : A -> C), F(f) : F(A) -> F(B) and F(g) : F(B) -> F(C) and F(f;g) : F(A) -> F(C) and F(f;g) = F(f) ; F(g) (also, if id_A : A -> A is the identity on A, the F(id_A) : F(A) -> F(A) is the identity on F(A) ) ' (in case they are unfamiliar with the notation f : A -> B , then this can be explained in each of the first few examples.) I guess it might also be good to give some counterexamples, and point out how the counterexamples fail to be functors, and why they are also not nice.