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I would highly recommend the book book by Bartosz Milewski "Category Theory for Programmers" which goes into some detail about Monads from a Category Theoretic perpective. And it's also available freely online : https://bartoszmilewski.com/2014/10/28/category-theory-for-programmers-the-preface/


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One possible formulation is that a monad transformer is a pointed endofunctor in the category of monads. This, however, excludes the continuation monad, the codensity monad, and possibly some other monad transformers. Full details are worked out in Chapter 14 of the book "The Science of Functional Programming". https://github.com/winitzki/sofp


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