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Virtual Topology and Functor Geometry

Virtual Topology and Functor Geometry by Fred Van Oystaeyen
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FOREWORD
INTRODUCTION
PROJECTS

A TASTE OF CATEGORY THEORY
Basic Notions
Grothendieck Categories
Separable Functors

NONCOMMUTATIVE SPACES
Small Categories, Posets, and Noncommutative Topologies
The Topology of Virtual Opens and Its Commutative Shadow
Points and the Point Spectrum: Points in a Pointless World
Presheaves and Sheaves over Noncommutative Topologies
Noncommutative Grothendieck Topologies
The Fundamental Examples I: Torsion Theories
The Fundamental Examples II: L(H)
Ore Sets in Schematic Algebras

GROTHENDIECK CATEGORICAL REPRESENTATIONS
Spectral Representations
Affine Elements
Quotient Representations
Noncommutative Projective Space

SHEAVES AND DYNAMICAL TOPOLOGY
Introducing Structure Sheaves
Dynamical Presheaves and Temporal Points
The Spaced-Time Model

BIBLIOGRAPHY
INDEX
CRC Press; November 2007
170 pages; ISBN 9781420060577
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Title: Virtual Topology and Functor Geometry
Author: Fred Van Oystaeyen
 
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