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Asked: 2026-05-26T05:07:04+00:00

If I find out that something is a Monoid or Monad , I get

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If I find out that something is a Monoid or Monad, I get all to use all kinds of fun functions, like foldMap, sequence or even mapM. They make me happy.

What do I get if I find out that something is a Category? Do I get anything fun besides overloading id and (.) ?

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  1. Editorial Team

    Do I get anything fun besides overloading id and (.) ?

    Well, you also (should) get the laws associated with them:

    "identity/left" forall p .
                id . p = p
"identity/right"        forall p .
                p . id = p
"association"   forall p q r .
                (p . q) . r = p . (q . r)

    As a side note:
    The reason that you don’t get that many fun functions like mapM or foldMap is, that saying something is a category is actually saying very little about it. The most useful functions I guess are the ones defined in Control.Category, which sometimes make code easier to read: >>> and <<<

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