Abstract
Publisher Summary This chapter discusses the models for synthetic differential geometry (SDG) and provides an intrinsic naive axiomatization of differential geometry as a foundation for synthetic reasoning in this field. The fundamental assumption, the Kock–Lawvere axiom, is inconsistent with classical logic; therefore, no set-theoretical models exist for this theory. However, topos-theoretical models have been constructed, showing, in particular, the compatibility of SDG with intuitionistic logic. The chapter presents construction, which is based on the algebraic theory, of categories of set-valued functors of the form Sets A , which are models of the Kock–Lawvere axiom as well as the axiom of integration of Kock–Reyes.
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