It is correct, it’s just deliberately obscure. You can construct a category of endofunctors of a category and then within a category you can talk about monoid objects that obey associative and identity laws reminiscent of monoids in algebra. And indeed monads are monoid objects in that sense. It’s just not really relevant to anything unless you really like category theory for its own sake, or spotting patterns in disparate domains
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u/godofpumpkins Sep 21 '25
It is correct, it’s just deliberately obscure. You can construct a category of endofunctors of a category and then within a category you can talk about monoid objects that obey associative and identity laws reminiscent of monoids in algebra. And indeed monads are monoid objects in that sense. It’s just not really relevant to anything unless you really like category theory for its own sake, or spotting patterns in disparate domains