> Category theory is really the mathematics of abstraction
Mathematics is the mathematics of abstraction. That's all you're doing in math, from the beginning to the end. What's the same between "I have two sheep in this pen and five in that one" and "I have two apples in this basket and five in that one"? Hmm, you can abstract out 2+5=7, since it works the same in both contexts.
Everything in math is creating and exploring abstractions. The good ones tend to stick around, the bad ones tend to be forgotten.
Category theory is the mathematics of composition. How much knowledge can you throw away and create reusable patterns of composition? How many interesting things can you find by adding back the smallest bits of additional structure on top of that minimum? How well do those things compose together, anyway?
> Category theory is the mathematics of composition.
I don't know why you're being downvoted (tone?) but you're right. Categories formalize exactly and only the notion of composition; its power is that this notion appears everywhere when you know what to look for. Most mathematical abstractions have composition baked in at one level or another, so I think the author should be pardoned for their phrasing; but I find yours more enlightening.
algebra of typed composition, a discipline for making definitions, study of universal properties, theory of duality, formal theory of analogy, mathematical model of mathematical models, inherently computational, science of analogy, mathematical study of (abstract) algebras of functions, general mathematical theory of structures,
Mathematics is the mathematics of abstraction. That's all you're doing in math, from the beginning to the end. What's the same between "I have two sheep in this pen and five in that one" and "I have two apples in this basket and five in that one"? Hmm, you can abstract out 2+5=7, since it works the same in both contexts.
Everything in math is creating and exploring abstractions. The good ones tend to stick around, the bad ones tend to be forgotten.
Category theory is the mathematics of composition. How much knowledge can you throw away and create reusable patterns of composition? How many interesting things can you find by adding back the smallest bits of additional structure on top of that minimum? How well do those things compose together, anyway?