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It helps you build an intuition for categories, if you're used to graphs :) If you have a working intuition for categories then in most cases the specific form
by Twey 1y ago
It helps you build an intuition for categories, if you're used to graphs :)
If you have a working intuition for categories then in most cases the specific formulation you choose as a foundation doesn't matter, just as most mathematicians work nominally in set theory without worrying about the subtleties of ZFC.
- sesm 1y agoIMO the right intuition about a tool comes from applying it in the context where it provides a real leverage. In case of Category Theory that would be advanced algebraic topology (not re-phrasing basic things which are easier to understand without CT).
- Twey 1y agoRephrasing things is useful when it allows you to draw equivalences with other things that might have results or insights that translate across, which is something a lot of people use CT for. As with most maths the payoffs aren't always immediate, though, which leads to a lot of frustration with from programmers who expect immediate results from their insights. From a programming perspective, though, a fair few important things have (by now) turned out to be useful that have come as a result of rephrasing programming in mathematical terms. Some top contenders are monads (directly from CT — think Haskell, but also LINQ, JavaScript Thenables, async/await, Rust Option/Result combinators, parser combinators), proof assistants and modern approaches to type systems, linear/substructural logic (think Rust or C++ move semantics), functional programming (which is now embraced at least to some extent by all mainstream programming languages), functional reactive programming (the core ideas behind things like React), et cetera.