Germ representability and local integration of vector fields in a well adapted model of SDG
The primary example of a ``well-adapted'' model of synthetic differential geometry is the topos G constructed by the author [Am. J. Math. 103, 683- 690 (1981; Zbl 0483.58003)]. There is a full embedding of the category of paracompact \(C^{\infty}\)-manifolds into G, which preserves transversal pullbacks and open covers. The article under review shows that the real line object R in G satisfies two additional axioms of interest: a germ representability axiom and an axiom for the local (infinitesimal) integration of vector fields. After reviewing the construction of G and some facts about Penon opens in G, the author proceeds to develop and prove these axioms. Some of these ideas are pursued at greater length in the author's joint work with \textit{M. Bunge} [Mathematical logic and theoretical computer science, Lect. Notes Pure Appl. Math. 106, 93-159 (1987; Zbl 0658.18004)].
scientific article; zbMATH DE number 4150469