Abstract

Until now we have encountered with various kinds of notions of infinitesimals. In this talk we will develop a systematic approach towards a general notion of infinitesimals using Weil algebras. This will enable us to generalize the K-L axiom to the Kock-Wraith axiom schema and to give the definition of a microlinear space. The category of microlinear spaces is a Cartesian closed full subcategory of our smooth universe closed under all small limits. Moreover, the category of microlinear spaces provides a very general and very convenient framework for the geometry of infinitesimals, which we will develop in the next talks beginning with tangent vectors and the tangent bundle.