The author does a superb job, particular when using a permutation domain to a binary domain in the first example.
The three tenets are clearly motivated: that the closure notion is sustained between G the group and H the subgroup even when the group operators are distinct as in f3; that the set types of G and H may or may not be the same; and then epi-/mono-/iso-morphism build up much like sur-/inj-/bi-jection build up.
As I remember, we get a quick lesson on it when I was 13/14. I can remember the room now. We were our (new) math teachers first ever class (and he actually took all the way through to 18).
It’s just so clearly laid out in this article, without the faffy stuff from textbooks or research papers.
I think Il summarize when he captured about ideals, kernels, and co-kernels too. Once one thinks of H in terms of parity matrices for dual spaces. ..and then sum-product algorithms and conditional probabilities for inference, it all becomes rather more interesting!