(Co)end Calculus
Seiten
2021
Cambridge University Press (Verlag)
978-1-108-74612-0 (ISBN)
Cambridge University Press (Verlag)
978-1-108-74612-0 (ISBN)
This easy-to-cite handbook gives the first systematic treatment of the (co)end calculus, a powerful tool for clarifying and simplifying many results in category theory that may then be exported to diverse mathematical fields. It is suitable as a reference for category theorists and users of category theory alike.
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.
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.
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.
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.
| Erscheinungsdatum | 22.07.2021 |
|---|---|
| Reihe/Serie | London Mathematical Society Lecture Note Series |
| Zusatzinfo | Worked examples or Exercises |
| Verlagsort | Cambridge |
| Sprache | englisch |
| Maße | 150 x 230 mm |
| Gewicht | 490 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| Mathematik / Informatik ► Mathematik ► Logik / Mengenlehre | |
| ISBN-10 | 1-108-74612-8 / 1108746128 |
| ISBN-13 | 978-1-108-74612-0 / 9781108746120 |
| Zustand | Neuware |
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