Synopses & Reviews
The book offers categorical introductions to order, topology, algebra and sheaf theory, suitable for graduate students, teachers and researchers of pure mathematics.
Synopsis
The book gives a categorical introduction to some of the key areas of modern mathematics. Researchers, teachers and graduate students in algebra and topology familiar with the very basic notions of category theory will find all the advanced tools needed for their subjects, without being forced to study category theory for its own sake. Rather, each of the eight largely independent chapters takes the reader on a journey through a particular subject, showing the power and applicability of the categorical foundations in each case.
Table of Contents
Introduction Walter Tholen; 1. Ordered sets via adjunction R. J. Wood; 2. Locales Jorge Picado, Ales Pultr and Anna Tozzi; 3. A functional approach to general topology Maria Manuel Clementino, Eraldo Giuli and Walter Tholen; 4. Regular, protomodular and abelian categories Dominique Bourn and Marino Gran; 5. Aspects of monads John MacDonald and Manuela Sobral; 6. Algebraic categories Maria Cristina Pedicchio and Fabrizio Rovatti; 7. Sheaf theory Claudia Centazzo and Enrico M. Vitale; 8. Beyond barr exactness: effective descent morphisms George Janelidze, Manuela Sobral and Walter Tholen.