# Conceptual Mathematics: A First Introduction to Categories

Cambridge University Press, Jul 30, 2009 - Mathematics - 390 pages
In the last 60 years, the use of the notion of category has led to a remarkable unification and simplification of mathematics. Conceptual Mathematics introduces this tool for the learning, development, and use of mathematics, to beginning students and also to practising mathematical scientists. This book provides a skeleton key that makes explicit some concepts and procedures that are common to all branches of pure and applied mathematics. The treatment does not presuppose knowledge of specific fields, but rather develops, from basic definitions, such elementary categories as discrete dynamical systems and directed graphs; the fundamental ideas are then illuminated by examples in these categories. This second edition provides links with more advanced topics of possible study. In the new appendices and annotated bibliography the reader will find concise introductions to adjoint functors and geometrical structures, as well as sketches of relevant historical developments.

### What people are saying -Write a review

#### Review: Conceptual Mathematics: A First Introduction To Categories

User Review  - Úlfar - Goodreads

Great book on category theory with well thought out explanations. It came up in Amazon 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. Read full review

#### Review: Conceptual Mathematics: A First Introduction To Categories

Great book on category theory with well thought out explanations. It came up in Amazon 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. Read full review

### Contents

 Galileo and multiplication of objects IUJUJUJ 3 Session 4 The category of sets 11 Session 13 Session 16 Deﬁnition of category 21 Session 24 Session 30
 68 168 Monoids 170 Paths 196 Elementary universal mapping properties 211 Terminal objects 225 Universal mapping properties and incidence relations 245 135 280 Binary operations and diagonal arguments 302

 Composing maps and counting maps 31 Session 9 34 The algebra of composition 37 Special properties a map may have 59 Quiz 60 Sections and retractions 68 Two general aspects or uses of maps 81 Two abuses of isomorphisms 89 Retracts and idempotents 99 Comparing inﬁnite sets 106 Composition of opposed maps 114 Session 10 120 Ascending to categories of richer structures 152 Categories of diagrams 161
 70 308 Higher universal mapping properties 311 81 315 LIIAUJNH 320 Map object versus product 328 The contravariant parts functor 335 Toposes 348 The Connected Components Functor 358 Constants codiscrete objects and many connected objects 366 Adjoint functors with examples from graphs and dynamical systems 372 The emergence of category theory within mathematics 378 136 385 86 386 Copyright