Reddit reviews Category Theory (Oxford Logic Guides)

Types and Programming Languages by Benjamin Pierce covers type theory, and systems of type inference that we can have, and the ones we can't and why.

Pearls of Functional Algorithm Design by Richard Bird covers how to think equationally about code. It is probably the best guide out there on how to "think" like a Haskeller. Not directly about a discipline of math you can apply, but the mindset is invaluable.

Wadler's original papers on monads are probably when they finally clicked for me.

The original Idiom paper is also a golden resource for understanding the motivation behind applicatives.

Jeremy Gibbons' The Essence of the Iterator Pattern motivates Traversable, which so nicely encapsulates what folks meant by mapM over the years.

Uustalu and Vene's The Essence of Dataflow Programming captures a first glimmer of how and why you might want to use a comonad, but it can be fairly hard reading.

Awodey's Category Theory is probably the best general purpose category theory text book.

For folks weak on the math side Lawvere and Schanuel's Conceptual Mathematics can be used to bootstrap up to Awodey and provides a lot of drill for the areas it covers.

Dan Piponi's blog is excellent and largely set the tone for my own explorations into Haskell.

For lenses the material is a bit more sparse. The best theoretical work in this space I can point you to is by Mike Johnson and Bob Rosebrugh. (Pretty much anything in the last few papers linked at Michael's publication page at Macquarie will do to get started). I have a video out there as well from New York Haskell. SPJ has a much more gentle introduction on Skills Matter's website. You need to signup there to watch it though.

For comonads you may get some benefit out of my site comonad.com and the stuff I have up on FP Complete, but you'll need to dig back a ways.

His book on Category Theory is also really good if anyone is interested in learning more. I'm reading it now myself.