This is the first self-contained introduction to the use of string diagrams to reason in elementary category theory. Written in an informal expository style, it features hundreds of carefully chosen diagrams to aid understanding. With numerous worked examples and exercises, the text is ideal for graduate students and advanced undergraduates.
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.
Arvustused
'String diagrams have proven an indispensable tool in modern category theory, enabling intuitive graphical reasoning while doing away with much of the bookkeeping that tends to bog down equational arguments. This textbook introduces category theory by way of string diagrams, making it an excellent choice both for beginners in category theory, as well as for more experienced category theorists seeking to add string diagrammatic reasoning to their repertoire.' Robin Kaarsgaard, University of Edinburgh '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
Muu info
The first introductory account of using string diagrams to reason in elementary category theory.
Prologue;
1. Category theory;
2. String diagrams;
3. Monads;
4. Adjunctions;
5. Putting it all together; Epilogue; Appendix. Notation; References; Index.
Ralf Hinze is Professor of Software Engineering at the University of KaiserslauternLandau (RPTU). His research is centered around the construction of provably correct software, with a particular emphasis on functional programming, algebra of programming, applied category theory, and persistent data structures. His goal is to develop theory, languages, and tools that simplify the construction of reliable software systems. Dan Marsden is a theoretical computer scientist currently working as Transitional Assistant Professor at the University of Nottingham. He is interested in the foundations of computer science, logic, and mathematics, with particular emphasis on the application of category theory.
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