© 2010

Towards Higher Categories

  • John C. Baez
  • J. Peter May


  • Thorough but informal guide to the theory of higher categorical structures


Part of the The IMA Volumes in Mathematics and its Applications book series (IMA, volume 152)

Table of contents

  1. Front Matter
    Pages i-xii
  2. John C. Baez, Michael Shulman
    Pages 1-68
  3. Julia E. Bergner
    Pages 69-83
  4. Stephen Lack
    Pages 105-191
  5. Lawrence Breen
    Pages 193-235
  6. Back Matter
    Pages 1-19

About this book


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.


Algebraic topology Category theory Cohomology Higher Categories Homotopy homology homotopical algebra

Editors and affiliations

  • John C. Baez
    • 1
  • J. Peter May
    • 2
  1. 1.Dept. MathematicsUniversity of California, RiversideRiversideU.S.A.
  2. 2.Dept. MathematicsUniversity of ChicagoChicagoU.S.A.

Bibliographic information