Models for Smooth Infinitesimal Analysis

1. Front Matter

   Pages i-x

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2. Introduction

   • Ieke Moerdijk, Gonzalo E. Reyes

   Pages 1-14

3. C ^∞-Rings

   • Ieke Moerdijk, Gonzalo E. Reyes

   Pages 15-55

4. C ^∞-Rings as Variable Spaces

   • Ieke Moerdijk, Gonzalo E. Reyes

   Pages 57-96

5. Two Archimedean Models for Synthetic Calculus

   • Ieke Moerdijk, Gonzalo E. Reyes

   Pages 97-131

6. Cohomology and Integration

   • Ieke Moerdijk, Gonzalo E. Reyes

   Pages 133-180

7. Connections on Microlinear Spaces

   • Ieke Moerdijk, Gonzalo E. Reyes

   Pages 181-237

8. Models with Invertible Infinitesimals

   • Ieke Moerdijk, Gonzalo E. Reyes

   Pages 239-292

9. Smooth Infinitesimal Analysis

   • Ieke Moerdijk, Gonzalo E. Reyes

   Pages 293-344

10. Back Matter

    Pages 345-399

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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.

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

• Mathematical Institute, University of Utrecht, Utrecht, The Netherlands

  Ieke Moerdijk

• Department of Mathematics, University of Montreal, Montreal, Canada

  Gonzalo E. Reyes

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