Categorical Foundations: Special Topics in Order, Topology, Algebra, and Sheaf Theory

ISBN-13: 9780521834148 / Angielski / Twarda / 2003 / 442 str.

Maria Pedicchio; Walter Tholen; G. -C Rota

Opis

Researchers, teachers and graduate students in algebra and topology--familiar with the very basic notions of category theory--will welcome this categorical introduction to some of the key areas of modern mathematics, without being forced to study category theory. Rather, each of the eight largely independent chapters analyzes a particular subject, revealing the power and applicability of the categorical foundations in each case.

Recenzje

'The book will be very useful for graduate students and teachers, and inspiring for the researchers interested in the discussed topics as well as in category theory itself.' EMS Newsletter

Spis treści

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.