Category Theory, Syntactically (2016)

Re:Category Theory, Syntactically (2016) by alipang on Thursday April 27, 2017 @10:29AM (#14211689)

I'd say there is not much point to Category Theory if we where to restrict ourselves to a single category. For instance Monoids are categories (with a single object) that is not the category of functions. Another set are the Kleisli Categories[1] that are equivalent to monads.

You mention Applicative Functors, which form another (different) category where arrows from a to b are on the form `f (a -> b)` and composition and identity laws of these arrows are equivalent to the applicative laws.

[1] https://en.wikipedia.org/wiki/Kleisli_category

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Re:Category Theory, Syntactically (2016) by a-saleh on Thursday April 27, 2017 @11:01AM (#14212010)

I got my point about single category from a friend of mine that studied category theory and applied it to problems topology.

Way he explained it, they often were searching for relations between categories that didn't at all intersect.

And way I was learning the applications of category theory in i.e. haskel, I viewed it more as learning about algebraic structures in the category of haskel types and functions.

So right now I have reasonable idea about i.e. applicative functors in haskel. But thinking about applicative functors as their own category is one abstraction step above what I am usually used to :-)

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