Models for smooth infinitesimal analysis

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Bibliographic Information

Models for smooth infinitesimal analysis

Ieke Moerdijk, Gonzalo E. Reyes

Springer-Verlag, c1991

  • : New York
  • : Berlin

Available at  / 31 libraries

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Note

Includes bibliographical references and index

Description and Table of Contents

Volume

: New York ISBN 9780387974897

Description

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.

Table of Contents

I C?-Rings.- II C?-Rings as Variable Spaces.- III Two Archimedean Models for Synthetic Calculus.- IV Cohomology and Integration.- V Connections on Microlinear Spaces.- VI Models with Invertible Infinitesimals.- VII Smooth Infinitesimal Analysis.- Appendix 1: Sheaves and Forcing.- 1 Sites.- 2 Sheaves.- 3 Forcing.- Appendix 2: A survey of models.- Appendix 3: The integration axiom.- Appendix 4: The amazing right adjoint.- Appendix 5: Comments, References and Further Developments.- Index of symbols.
Volume

: Berlin ISBN 9783540974895

Description

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 and applied. By discussing topics such as integration, cohomology and vector bundles in this context, the adequacy of these spaces for analysis and geometry is illustrated and the connection with the classical approach to C-manifolds is explained.

Table of Contents

  • C-rings
  • C-rings as variable spaces
  • two Archimedean models for synthetic calculus
  • cohomology and integration
  • connections on microlinear spaces
  • models with invertible infinitesimals
  • smooth infinitesimal analysis. Appendices: Sheaves and forcing
  • a survey of models
  • the integration axiom
  • the amazing right adjoint
  • comments, references and further developments.

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