# Conceptual Mathematics: A First Introduction To Categories

Conceptual Mathematics A First Introduction To Categories The idea of a category a sort of mathematical universe has brought about a remarkable unification and simplification of mathematics Written by two of the best known names in categorical logic this is

• Title: Conceptual Mathematics: A First Introduction To Categories
• Author: F. William Lawvere Stephen H. Schanuel
• ISBN: 9780521478175
• Page: 217
• Format: Paperback
• The idea of a category a sort of mathematical universe has brought about a remarkable unification and simplification of mathematics Written by two of the best known names in categorical logic, this is the first book to apply categories to the most elementary mathematics.

#### 331 Comment

• M says:

A real gem. More than an introduction to categories, if you stick with it this is an introduction to topos theory, and more generally an invitation to Lawvere-space. In other words, the treatment is largely synthetic (as opposed to analytic). Brouwer's fixed point theorem is a lovely payoff 1/3rd of the way through, and the Lawvere fixed point theorem that comes later, even better – if the treatment of dynamical systems etc. wasn't a thrill enough for the reader of what is in some respects a t [...]

• Úlfar says:

Great book on category theory with well thought out explanations. It came up in recommendations when I was browsing for Haskell books and I thought I would give it a try. It was an enlightening read. I finally understand the pure mathematical power of category theory after reading this book.

• Walter says:

Many people think of mathematics as the operations like addition, subtraction, multiplication or division, or the complicated models used in calculus, linear modeling or differential equations. But mathematics embodies conceptual tools that are as important to understanding math as any other branch of the science. In this work, the authors lay out the concepts of conceptual mathematics in a way that is very understandable to students and to self-learners. Conceptual mathematics is sort of the br [...]

• Mark says:

The first 100 pages or so I really enjoyed, but after that, the book gradually became increasingly difficult to follow.It seems clear that it's written by two authors; it consists alternatingly of 'articles' and 'sessions', and the sessions are much easier to follow than the articles. Even so, as the text advances, it becomes clear why Category Theory is also known as Abstract Nonsense (although I do realise that there's supposedly no negative charge in that term).

• DJ says:

low level intro to category theory that is uniquely accessible to undergrads

• Stuart says:

Got to Article 3, Session 11, Exercise 1 and had to put it down for a while. It's an ok book, but not great for learning (for me, at least)

• Dave Peticolas says:

My first attempt to understand what the Haskell folks are really up to. I have a feeling many more attempts will be required!

• Chris says:

Definitely the most accessible introduction to category theory in existence.