(Co)end Calculus

This easy-to-cite handbook gives the first systematic treatment of the (co)end calculus in category theory and its applications.

Fosco Loregian (Author)

9781108746120, Cambridge University Press

Paperback / softback, published 22 July 2021

330 pages
23 x 15 x 1.8 cm, 0.49 kg

'At just above 300 pages, this book achieves a great deal in a limited space. …The presentation is lively and the author's enthusiasm for exposition comes across vividly, making the book a pleasant read.' Nicola Gambino, MathSciNet

The language of ends and (co)ends provides a natural and general way of expressing many phenomena in category theory, in the abstract and in applications. Yet although category-theoretic methods are now widely used by mathematicians, since (co)ends lie just beyond a first course in category theory, they are typically only used by category theorists, for whom they are something of a secret weapon. This book is the first systematic treatment of the theory of (co)ends. Aimed at a wide audience, it presents the (co)end calculus as a powerful tool to clarify and simplify definitions and results in category theory and export them for use in diverse areas of mathematics and computer science. It is organised as an easy-to-cite reference manual, and will be of interest to category theorists and users of category theory alike.

Preface
1. Dinaturality and (co)ends
2. Yoneda and Kan
3. Nerves and realisations
4. Weighted (co)limits
5. Profunctors
6. Operads
7. Higher dimensional (co)ends
Appendix A. Review of category theory
Appendix B
References
Index.

Subject Areas: Algebraic topology [PBPD], Algebraic geometry [PBMW], Calculus & mathematical analysis [PBK], Set theory [PBCH], Mathematical logic [PBCD]