Name: Category Theory in Context
ISBN: 9780486809038

Category Theory in Context

Category theory has provided the foundations for many of the twentieth century's greatest advances in pure mathematics. This concise, original text for a one-semester course on the subject is derived from courses that author Emily Riehl taught at Harvard and Johns Hopkins Universities. The treatment introduces the essential concepts of category theory: categories, functors, natural transformations, the Yoneda lemma, limits and colimits, adjunctions, monads, and other topics. Suitable for advanced undergraduates and graduate students in mathematics, the text provides tools for understanding and attacking difficult problems in algebra, number theory, algebraic geometry, and algebraic topology. Drawing upon a broad range of mathematical examples from the categorical perspective, the author illustrates how the concepts and constructions of category theory arise from and illuminate more basic mathematical ideas. Prerequisites are limited to familiarity with some basic set theory and logic.

What Hacker News says

363849473754Jul 2026

For a more advanced book: Category Theory in Context by Emily Riehl

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eointierneyMar 2022

Read books

I'm not joking, it's the best antidote to the thought-theft of "social media". Pick a subject in which you're interested, find a representively excellent text, and read. And then re-read, because unless you're a genius you won't absorb everything first time.

Also it's wonderful to just curl up with a book and a cup of tea and let time pass you by as you ... learn the considered thought of others! This is civilised!

Normally I'd recommend history but around these parts Category Theory in Context by Emily Riehl is probably acceptable :)

About re-reading, especially textbooks: it takes time and trouble to appreciate the difficult and often esoteric ideas represented in a text and understand the underlying deep thought. The author(s) wrote and re-wrote every damn phrase in terms of their imagined audience. The first pass yields a basic familiarity, but try every chapter again in light of the later insights.

I remember the first time I read Introduction to Metamathematics by Kleene, and I remember the fourth time so much better. I can feel the cloth binding, I can hear his voice clearly.

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cg30eNov 2021

For sure. I'll list some books for introduction to proofs, abstract algebra, real analysis, topology and category theory. These are not comprehensive, just listing books off the top of my head. I'll definitely be leaving off personal favorites other people have. You'll like some better than others. Some of these are beginner books and some are more advanced. A good tutor can help you get through the more advanced books. I tried to list the most beginner friendly book first in the list under each subject. Then the more advanced books later in the list.

Introduction to Proofs:

Just pick one of these that speaks to you the most. All three are good.

Discrete Mathematics with Applications - Epp

Discrete Mathematics and Its Applications - Rosen

Mathematical Proofs: A Transition to Advanced Mathematics - Chartrand, et al.

Abstract Algebra:

How to Think about Abstract Algebra - Alcock

Abstract Algebra - Pinter

Abstract Algebra: A First Course - Saracino

Algebra - Artin

Abstract Algebra - Herstein

Abstract Algebra - Dummit & Foote

Linear Algebra:

Maybe an engineering based book first if you haven't seen linear algebra in a while (e.g. Strang or Linear Algebra: Step by Step by Singh).

Then:

Linear Algebra - Friedberg, et al

Linear Algebra Done Right - Axler

Linear Algebra - Hoffman & Kunze

Real Analysis:

How to Think About Analysis - Alcock

Understanding Analysis - Abbott

Tao's Analysis text

Principles of Mathematical Analysis - Rudin

Topology:

Topology - Munkres

Topology A Categorical Approach - Tai-Danae Bradley, Tyler Bryson, and John Terilla

Check out this list:

http://pi.math.cornell.edu/~hatcher/Other/topologybooks.pdf for others.

Category theory:

Categories and Toposes: Visualized and Explained - Southwell

Conceptual Mathematics: A First Introduction to Categories - Lawvere

Category Theory for Programmers - Milewski (if you like functional programming)

Programming with Categories - Fong, Milewski, Spivak (if you like functional programming)

Category Theory in Context - Riehl

There are a few others by Spivak which you may like.

If you don't know category theory whatsoever then I like Southwell the best (pair them up with his youtube videos). Eugenia Cheng also has a nice set of lecture videos.

If you already know math pretty well, then Riehl is a favorite.

Hope that helps!

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benrbrayJun 2021

Riehl's "Category Theory in Context" is great. It's one of those books where every page really takes a couple hours to fully absorb. It pairs well with Milewski's "Category Theory for Programmers" [1] series, which is comparatively lighter and gives some concrete examples.

[1] https://bartoszmilewski.com/2014/10/28/category-theory-for-p...

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benrbrayApr 2021

If you’re curious about this stuff and don’t know where to begin, the first chapter of Fong & Spivak, “An Invitation to Applied Category Theory: Seven Sketches in Compositionality” [1] also introduces category-theoretic ideas using partial orders.

Edit: After the Fong & Spivak book, the book by Emily Riehl, "Category Theory in Context" is an excellent next step, although it requires some mathematical maturity.

[1]: https://arxiv.org/abs/1803.05316

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ABeeSeaApr 2021

Category Theory in Context is such a great book. Kudos to Dover’s Aurora publishing arm for a great, original book at such a great price. Always love dover and adding additional new contents to the back catalogue of reprints is amazing.

The book does constantly reference other branches of mathematics (algebra, topology, etc) for example. Probably not strictly necessary to have that background to follow the book, but helpful.

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