C ∞-Rings as Variable Spaces

Ieke Moerdijk and Gonzalo E. Reyes
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Ieke Moerdijk: University of Utrecht, Mathematical Institute
Gonzalo E. Reyes: University of Montreal, Department of Mathematics

Chapter Chapter II in Models for Smooth Infinitesimal Analysis, 1991, pp 57-96 from Springer

Abstract: 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).

Keywords: Variable Space; Open Cover; Natural Transformation; Weil Algebra; Opposite Category (search for similar items in EconPapers)
Date: 1991
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DOI: 10.1007/978-1-4757-4143-8_3

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