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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.
This book provides foundational background for advanced study in higher category theory, focusing on motivations and key structures. It begins with an exploration of how algebraic topology tools are viewed through the lens of n-category theory, followed by surveys of (infinity,1)-categories and the algebraic modeling of homotopy n-types. The primary emphasis is placed on the theory of bicategories, which serves as a crucial starting point for understanding more complex higher categorical structures. The book also includes discussions on gerbes in differential geometry and the historical development of category theory in Australia.
This collection of articles serves as a preparatory text for those interested in higher category theory, offering insights into its motivations and fundamental concepts. The inclusion of survey articles on well-understood areas like (infinity,1)-categories and homotopy n-types, alongside a detailed look at bicategories, suggests a structured approach to introducing complex topics. The book's dedication to Max Kelly and the inclusion of historical context indicate an appreciation for the field's development. The diverse range of topics, from algebraic topology to differential geometry, points to a broad yet focused exploration of higher categorical structures.
Page Count:
268
Publication Date:
2010-01-01
ISBN-10:
1441915230
ISBN-13:
9781441915238
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