Towards higher categories
By: John C. Baez, J. Peter May, editors
Series: The IMA volumes in mathematics and its applications -- v. 152; IMA volumes in mathematics and its applications -- v. 152.
Publisher: Springer
Published: 2010
Place of publication: New York
Language: eng
Number of pages: 268
ISBN-13: 9781441915238
Subjects: Categories (Mathematics); Kategorie (Mathematik)
Description: The purpose of this book is to give background for those who would like to delve into some higher category theory. It is not a primer on higher category theory itself. It begins with a paper by John Baez and Michael Shulman which explores informally, by analogy and direct connection, how cohomology and other tools of algebraic topology are seen through the eyes of n-category theory. The idea is to give some of the motivations behind this subject. There are then two survey articles, by Julie Bergner and Simona Paoli, about (infinity,1) categories and about the algebraic modelling of homotopy n-types. These are areas that are particularly well understood, and where a fully integrated theory exists. The main focus of the book is on the richness to be found in the theory of bicategories, which gives the essential starting point towards the understanding of higher categorical structures. An article by Stephen Lack gives a thorough, but informal, guide to this theory. A paper by Larry Breen on the theory of gerbes shows how such categorical structures appear in differential geometry. This book is dedicated to Max Kelly, the founder of the Australian school of category theory, and an historical paper by Ross Street describes its development.
Notes: Includes bibliographical references.