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C ∞-Rings as Variable Spaces

In: Models for Smooth Infinitesimal Analysis

Author

Listed:
  • Ieke Moerdijk

    (University of Utrecht, Mathematical Institute)

  • Gonzalo E. Reyes

    (University of Montreal, Department of Mathematics)

Abstract

In this chapter we will consider the geometric aspect of C ∞-rings. As a first step, we will introduce the category L of loci or formal C ∞-varieties. These are just the duals of finitely generated C ∞- rings. This category L contains the usual category of manifolds, but also other useful objects such as infinitesimal spaces. However, function spaces can in general not be constructed in L. This is only possible when the domain space is sufficiently small (the dual of a Weil algebra).

Suggested Citation

  • Ieke Moerdijk & Gonzalo E. Reyes, 1991. "C ∞-Rings as Variable Spaces," Springer Books, in: Models for Smooth Infinitesimal Analysis, chapter 0, pages 57-96, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4757-4143-8_3
    DOI: 10.1007/978-1-4757-4143-8_3
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