English

Classifying toposes for some theories of $\mathcal{C}^{\infty}-$rings

Logic 2018-11-22 v1 Category Theory

Abstract

In this paper we present classifying toposes for the following theories: the theory of C\mathcal{C}^{\infty}-rings, the theory of local C\mathcal{C}^{\infty}-rings and the theory of von Neumann regular C\mathcal{C}^{\infty}-rings. The classifying toposes for the first two theories were stated without proof by Ieke Moerdijk and Gonzalo Reyes on the page 366 of \cite{MSIA}, where they assert that the topos SetCRngfp{\rm \bf Set}^{\mathcal{C}^{\infty}{\rm \bf Rng}_{\rm fp}} classifies the theory of C\mathcal{C}^{\infty}-rings and that the smooth Zariski topos classifies the theory of local C\mathcal{C}^{\infty}-rings.

Keywords

Cite

@article{arxiv.1811.08838,
  title  = {Classifying toposes for some theories of $\mathcal{C}^{\infty}-$rings},
  author = {Jean Cerqueira Berni and Hugo Luiz Mariano},
  journal= {arXiv preprint arXiv:1811.08838},
  year   = {2018}
}