Categories for the Working Mathematician

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1. l332mnSep 2021
   As a mathematician, I can't recommend "Categories for the Working Mathematician" enough, written by the (co)creator of category theory himself.
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2. definedApr 2017
   Honestly, Saunders MacLane's book, "Categories for the Working Mathematician", was very useful for this non-mathematician. It was surprisingly accessible if I started at the introduction and did not move forward until I grokked the content.

   I won't pretend I absorbed all (or even most) of it, but I at least understand the "Standard Haskell Joke" now (which is a funny misquote from his book)[1][2]. I also understand much more clearly why Haskell is so associated with Category Theory.

   [1]: "A monad is just a monoid in the category of endofunctors, what's the problem?"

   [2]: What MacLane actually wrote is:

   All told, a monad in X is just a monoid in the category of endofunctors of X, with product × replaced by composition of endofunctors and unit set by the identity endofunctor.

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3. telFeb 2015
   In my experience if you have or are willing to invest on the side to gain the necessary abstract algebra background then MacLane's Categories for the Working Mathematician is the go to source.

   It is certainly "for the Working Mathematician", so don't make bones about that, but to not include it in a reading list is criminal. If nothing else, buy it and keep rereading it from the beginning as a barometer for how much you're learning. As you penetrate it more and more you can judge that as meteoric increase in understanding.

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4. ihmJan 2015
   Lawvere and Schanuel's excellent "Conceptual Mathematics" has plenty of exercises, and the book is insanely approachable while still teaching a good amount (it's chock full of examples).

   Mac Lane (Categories for the Working Mathematician) also has exercises and I think the ones from the first few chapters aren't so hard.

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5. TimorousBestieAug 2026
   Instead of spending time beating one’s head against Russell and Whitehead, I would advise reading Homotopy Type Theory (aka the HoTT Book). Dependent types are cool and mind-expanding, but higher inductive types are downright mind-altering.

   The Little Schemer/Typer could be used as a preparatory text to gear one up for HoTT.

   It also has the advantage of being a bit more applicable to functional programming languages, maybe even more so than Mac Lane’s Categories for the Working Mathematician (which I sometimes see suggested to mathematically-inclined Haskell novices).

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6. fn-moteAug 2026
   > maybe even more so than Mac Lane’s Categories for the Working Mathematician (which I sometimes see suggested […])

   FWIW, I am very against this recommendation. That book is needlessly opaque. I don’t know a good recommendation for category theory, but that isn’t it.

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