ABSTRACT
Synthetic differential geometry (SDG) started by the consideration of an axiom of jet representability. This axiom is stated in a ringed elementary topos ( E https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003073055/18313969-4065-4025-b930-90a95587304e/content/eq736.tif"/> ,R). Briefly, it says that there is an object in E https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003073055/18313969-4065-4025-b930-90a95587304e/content/eq737.tif"/> , denoted Dr(n), which is the domain of definition for the r-jets of functions in n variables Rn → R. This axiom concerns the infinitesimal aspects of differential geometry. The aim of this paper is to consider a second axiom which establishes the capacity to pass from the infinitesimal to the local. This is an axiom of germ representability. Briefly, it says that there is an object in E https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003073055/18313969-4065-4025-b930-90a95587304e/content/eq738.tif"/> , denoted ⊿(n), which is the domain of definition for germs of functions in n variables Rn → R.
