Introducing String Diagrams
The Art of Category Theory

The first introductory account of using string diagrams to reason in elementary category theory.

Ralf Hinze (Author), Dan Marsden (Author)

9781009317863, Cambridge University Press

Hardback, published 10 August 2023

195 pages
24.4 x 17 x 1.3 cm, 0.518 kg

'Well-chosen notation plays a vital role in constructive calculation because it facilitates the exploitation of algebraic properties. This book's exemplary use of string diagrams in category theory will inspire and invigorate the calculational method. Peruse and ponder its colourful beauty.' Roland Backhouse, University of Nottingham

String diagrams are powerful graphical methods for reasoning in elementary category theory. Written in an informal expository style, this book provides a self-contained introduction to these diagrammatic techniques, ideal for graduate students and researchers. Much of the book is devoted to worked examples highlighting how best to use string diagrams to solve realistic problems in elementary category theory. A range of topics are explored from the perspective of string diagrams, including adjunctions, monad and comonads, Kleisli and Eilenberg–Moore categories, and endofunctor algebras and coalgebras. Careful attention is paid throughout to exploit the freedom of the graphical notation to draw diagrams that aid understanding and subsequent calculations. Each chapter contains plentiful exercises of varying levels of difficulty, suitable for self-study or for use by instructors.

Prologue
1. Category theory
2. String diagrams
3. Monads
4. Adjunctions
5. Putting it all together
Epilogue
Appendix. Notation
References
Index.

Subject Areas: Mathematical theory of computation [UYA]