There's not much to understand about CT, anyway: It's actually nearly
as trivial as set theory.
You mean that theory which predicts the existence of infinitely many infinities; in fact for any cardinal, there are at least that many cardinals? That theory in which aleph_1 and 2^aleph_0 are definitely comparable, but we provably cannot compare them? The theory which has omega_0 < omega_1 < omega_2 < ... omega_omega < ..., where obviously omega_a is much larger than a... except for when it catches its tail and omega_alpha = alpha for some crazy-ass alpha.
I don't think set theory is trivial in the least. I think it is complicated, convoluted, often anti-intuitive and nonconstructive.
Category theory is much more trivial, and that's what makes it powerful. (Although training yourself to think categorically is quite difficult, I'm finding)
One part of the benefit starts when you begin
to categorise different kind of categories, in the same way that
understanding monads is easiest if you just consider their difference
to applicative functors. It's a system inviting you to tackle a problem
with scrutiny, neither tempting you to generalise way beyond
computability, nor burdening you with formal proof requirements or
shackling you to some other ball and chain.
Sadly, almost all texts about CT are absolutely useless: They
tend to focus either on pure mathematical abstraction, lacking
applicability, or tell you the story for a particular application of CT
to a specific topic, loosing themselves in detail without providing the
bigger picture. That's why I liked that Rosetta stone paper so much: I
still don't understand anything more about physics, but I see how
working inside a category with specific features and limitations is the
exact right thing to do for those guys, and why you wouldn't want to do
a PL that works in the same category.
Throwing lambda calculus at a problem that doesn't happen to be a DSL
or some other language of some sort is a bad idea. I seem to understand
that for some time now, being especially fond of automata[1] to model
autonomous, interacting agents, but CT made me grok it. The future will
show how far it will pull my thinking out of the Turing tarpit.
[1] Which aren't, at all, objects. Finite automata don't go bottom in
any case, at least not if you don't happen to shoot them and their
health drops below zero.
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