Models for Smooth Infinitesimal Analysis

  • Ieke Moerdijk
  • Gonzalo E. Reyes

Table of contents

  1. Front Matter
    Pages i-x
  2. Ieke Moerdijk, Gonzalo E. Reyes
    Pages 1-14
  3. Ieke Moerdijk, Gonzalo E. Reyes
    Pages 15-55
  4. Ieke Moerdijk, Gonzalo E. Reyes
    Pages 57-96
  5. Ieke Moerdijk, Gonzalo E. Reyes
    Pages 97-131
  6. Ieke Moerdijk, Gonzalo E. Reyes
    Pages 133-180
  7. Ieke Moerdijk, Gonzalo E. Reyes
    Pages 181-237
  8. Ieke Moerdijk, Gonzalo E. Reyes
    Pages 239-292
  9. Ieke Moerdijk, Gonzalo E. Reyes
    Pages 293-344
  10. Back Matter
    Pages 345-399

About this book

Introduction

The aim of this book is to construct categories of spaces which contain all the C?-manifolds, but in addition infinitesimal spaces and arbitrary function spaces. To this end, the techniques of Grothendieck toposes (and the logic inherent to them) are explained at a leisurely pace and applied. By discussing topics such as integration, cohomology and vector bundles in the new context, the adequacy of these new spaces for analysis and geometry will be illustrated and the connection to the classical approach to C?-manifolds will be explained.

Keywords

Calc Finite Grothendieck topology addition calculus cohomology development forcing function function space geometry integration manifold techniques variable

Authors and affiliations

  • Ieke Moerdijk
    • 1
  • Gonzalo E. Reyes
    • 2
  1. 1.Mathematical InstituteUniversity of UtrechtUtrechtThe Netherlands
  2. 2.Department of MathematicsUniversity of MontrealMontrealCanada

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4757-4143-8
  • Copyright Information Springer-Verlag New York 1991
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4419-3095-8
  • Online ISBN 978-1-4757-4143-8
  • About this book