resource that explains vocabulary used in Edward Kmett's lens package

Question

I am trying to read the documentation in Edward Kmett's Lens package. I am not familiar with a lot of the terms used (profunctor, isomorphism, monomorphic, contravariant, bifunctor, etc...)

What would be a good resource to go to learn some of this vocabulary as it is used in this library.

Evictee

If you reword this question to ask what the origin or meaning of the vocabulary is it won't be confused as asking for an off-site resource. – Segno

I always liked Bartosz's series, bartoszmilewski.com/2014/10/28/… – Bochum

I found the lecture notes of "Category theory for the Sciences" on MIT OCW very useful. The (by now slightly renewed) textbook is also available in print with exercise solutions. – Baddie

Answer 1

These are terms from category theory. As for resources, Ed himself has some suggestions. Personally, I second his recommendations of Conceptual Mathematics by Lawvere and Awodey's Category Theory.

Bullroarer

They're a bit more advanced (relative to Conceptual Mathematics), but the Catsters videos can make a nice addition to Conceptual Mathematics and Category Theory. – Marishamariska

The Catsters videos are great! – Bullroarer

Definitely agreed! I've been reading Dr. Cheng's latest book (How to Bake π) and, even though it is written for a primarily non-mathematical audience, it does talk about some general ideas and terminology of category theory (along with some nice baking recipes) written in her entertaining, enthusiastic style. That could be another potential resource to get some ideas about the categorical way of looking at things and some categorical topics, but it is a bit less on the technical side. Also it has, in my opinion, a very effective and clear defense of (applied and pure) mathematics. – Marishamariska

@DavidYoung Her book on n-categories is also great. – Bullroarer