Loregian (Co)end Calculus

Erscheinungsjahr 2021
ISBN: 978-1-108-78860-1
Verlag: Cambridge University Press
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 0 Seiten

Reihe: London Mathematical Society Lecture Note Series

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.

Autoren/Hrsg.

Loregian, Fosco

Fachgebiete

• Mathematik | Informatik Mathematik Geometrie Algebraische Geometrie
• Mathematik | Informatik Mathematik Mathematik Allgemein Grundlagen der Mathematik
• Mathematik | Informatik Mathematik Topologie Algebraische Topologie
• Mathematik | Informatik Mathematik Mathematische Analysis
• Mathematik | Informatik Mathematik Mathematik Allgemein Mathematische Logik

Inhaltsverzeichnis

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.

Über Autor(innen)

Loregian, Fosco
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.