Review
3 stars
I read this book because a friend was excited about its claimed approach to category theory without math. The book positions itself as an accessible introduction to category theory that helps people who aren't so interested in the mathematical exactitude, but rather would like to learn by example. It claims that category theory can help people think more clearly about a range of issues, e.g. material science or neurobiology. It was that claim that I found intriguing.
I'd say the book fails by its own standards. It is very heavy on math, often unnecessarily though. It also does a very poor job of signposting throughout the book why it's proving the theorem it's currently proving. Ultimately, the central idea I took away from it was that the category of database schemas is isomorphic to the category of categories, so for the purpose of introducing categorical clarity of thinking into other …
I read this book because a friend was excited about its claimed approach to category theory without math. The book positions itself as an accessible introduction to category theory that helps people who aren't so interested in the mathematical exactitude, but rather would like to learn by example. It claims that category theory can help people think more clearly about a range of issues, e.g. material science or neurobiology. It was that claim that I found intriguing.
I'd say the book fails by its own standards. It is very heavy on math, often unnecessarily though. It also does a very poor job of signposting throughout the book why it's proving the theorem it's currently proving. Ultimately, the central idea I took away from it was that the category of database schemas is isomorphic to the category of categories, so for the purpose of introducing categorical clarity of thinking into other domains, it's probably best to get a really thorough understanding of database schemas.
If you want to read this book and skip all un-necessary math and only get the basic understanding that might be useful, here's the reading guide I'd propose:
Chapter 2: The Category of Sets Skip the set theory proofs if you have a working idea of basic set theory. Read the chapter for the introduction to diagrams and ologs.
Chapter 3: Fundamental Considerations in Set Read 3.1. Products and Coproducts, skim the rest
Chapter 4: Categories and Functors, Without Admitting It This is the first chapter that actually talks about categories. Read "4.1. Monoids" carefully, skip "4.2". Groups except for a basic understanding of what a group is, skim "4.3. Graphs" and "4.4 Orders" for the terminology, read "4.5 Databases" carefully.
Chapter 5 Basic Category Theory Read "5.1 Categories and Functors", skip "5.2. Common categories and functors", read "5.3. Natural Transformations" for a basic understanding, skip "5.4. Categories and Schemas are equivalent" except for the title.
Chapter 6 Fundamental Considerations of Categories skip
Chapter 7 Categories at work Read "7.3 Monads"
I've been finding "Category Theory for Programmers" much more helpful and much more true to the goal of avoiding math when not needed.