(Co)end Calculus

by Fosco Loregian

Overview

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.

Product Details

ISBN-13:	9781108746120
Publisher:	Cambridge University Press
Publication date:	07/22/2021
Series:	London Mathematical Society Lecture Note Series , #468
Pages:	330
Product dimensions:	5.91(w) x 9.06(h) x 0.71(d)

About the Author

Fosco Loregian is a postdoctoral researcher at Tallinn University of Technology, Estonia. His research is mainly focused on category theory and its applications in algebra, geometry and logic.

Table of Contents

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.

Editorial Reviews

'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

From the Publisher