Axiomatic differential geometry II-1 - vector fields

Abstract

In our previous paper entitled \Axiomatic dierential geometry I { to- wards model categories of dierential geometry, we have given a category-theoretic framework of dierential geometry. As the rst part of our series of papers concerned with dierential-geome tric developments within the above axiomatic scheme, this paper is devoted to vector elds. The principal result is that the totality of vector elds on a microlinear and Weil exponential object forms a Lie algebra.