Category Theory - books

Category Theory

There are two approaches to category theory, most books, such as those under 'expert' below assume quite a wide knowledge of mathematics. They give lots of examples from different structures to help the reader to 'abstract out' the categorical concepts.

Introduction

The following two books, both co-authored by F. William Lawvere, are aimed at relative newcomers to mathematics. Although they are not trivial and I think they are useful for a wide range of readers.

flag flag flag flag flag flag Conceptual Mathematics - This is a book about category theory that does not assume an extensive knowledge over a wide area of mathematics. The style of the book is a bit quirky though.
flag flag flag flag flag flag Sets for Mathematics - This is a book about sets from category theory point of view.

Expert

flag flag flag flag flag flag Categories for the Working Mathematician - This is the classic book on the subject but the pace is very quick and a wide knowledge of mathematics is required to understand the examples. Its hard going for me but then I'm not a working mathematician.
flag flag flag flag flag flag Categorical Theory - This book is a general introduction to the subject, a bit easier than the Saunders Mac Lane book but still very theoretical.

Category Theory and Logic

flag flag flag flag flag flag Introduction to Higher Order Categorical Logic - Lambek & Scott - Relates lambda calculus to higher order logic and cartesian closed categories.

Category Theory and Type Theory

flag flag flag flag flag flag Categorical Logic and Type Theory - This book is about logic, type theory and category theory. It assumes the reader is familiar with category theory concepts such as adjunctions, limits and CCCs.
flag flag flag flag flag flag Categories for Types - The book has some introductory material including a chapter about category theory (although it would be a steep learning curve with no other sources). Then the book shows how to represent category theory in type theory.

 


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Book Shop - Further reading.

Where I can, I have put links to Amazon for books that are relevant to the subject, click on the appropriate country flag to get more details of the book or to buy it from them.

flag flag flag flag flag flag The Princeton Companion to Mathematics - This is a big book that attempts to give a wide overview of the whole of mathematics, inevitably there are many things missing, but it gives a good insight into the history, concepts, branches, theorems and wider perspective of mathematics. It is well written and, if you are interested in maths, this is the type of book where you can open a page at random and find something interesting to read. To some extent it can be used as a reference book, although it doesn't have tables of formula for trig functions and so on, but where it is most useful is when you want to read about various topics to find out which topics are interesting and relevant to you.

 

Terminology and Notation

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