Two Archimedean Models for Synthetic Calculus

  • Ieke Moerdijk
  • Gonzalo E. Reyes

Abstract

In chapter II, we introduced the category of smooth functors \(Set{s^{{L^{op}}}}\) This category has good function spaces, infinitesimal spaces, convenient exactness properties, and it contains the usual category of manifolds M. Furthermore, the embedding \(M \to Set{s^{{L^{op}}}}\) preserves the good limits in M, namely tranversal pullbacks. Nevertheless, \(Set{s^{{L^{op}}}}\) has pathological properties: the smooth line R, which is a commutative ring with unit, is not even a local ring. Moreover, R is not Archimedean. From a somewhat different viewpoint, one can say that, besides some good limits, M also has good colimits, such as open covers. The trouble with \(Set{s^{{L^{op}}}}\) is that these covers are not preserved by the embedding \(M \to Set{s^{{L^{op}}}}\).

Keywords

Local Ring Open Cover Inverse Limit Left Adjoint Constant Sheaf 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 1991

Authors and Affiliations

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

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