Towards Higher Categories

Towards Higher Categories
Author: John C. Baez
Publisher: Springer Science & Business Media
Total Pages: 292
Release: 2009-09-24
Genre: Algebra
ISBN: 1441915362

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.

Recent Trends in Graph Theory

Recent Trends in Graph Theory
Author: M. Capobianco
Publisher: Springer
Total Pages: 218
Release: 2006-11-15
Genre: Mathematics
ISBN: 3540365087

These are the proceedings of the first graph theory conference held in New York City, on June 11-13, 1970, sponsored by St. John's University, Jamaica, New York. In spirit and scope it followed the graph theory conferences recently held in Ann Arbor and Kalamazoo: the contributors and participants were persons from Canada and the United States who are interested and very active in graph theory and its applications.

Symposium on Several Complex Variables. Park City, Utah, 1970

Symposium on Several Complex Variables. Park City, Utah, 1970
Author: Robert M. Brooks
Publisher: Springer
Total Pages: 244
Release: 2006-11-15
Genre: Mathematics
ISBN: 3540364552

This volume contains articles based on talks given at the Symposium on several complex variables, Park City, March 30 - April 3, 1970. The papers herein represent a broad spectrum of mathematical research (e.g. function algebras, sheaf theory, differential operators, manifolds) but are related by the fact that they are all related to some degree to the area of several complex variables.