# Some model theory with C^\infty-rings and Smooth Infinitesimal Analysis

In the first half of the talk I will speak about the general idea of how to construct models of the smooth world in which the category of smooth manifolds can be embedded in a nice way using certain subcategories of C^\infty-rings. In the second half we will turn to the naive theory and start to develop a smooth infinitesimal analysis using the Kock-Lawvere axiom. The corresponding sections in Lavendhomme’s book are 1.1.3,1.1.4 and 1.2.

This talk is part of the Synthetic Differential Geometry Seminar series.