A much larger class of Frolicher spaces than that of convenient vector spaces may embed into the Cahier topos

Abstract

It is well known that the category of Frolicher spaces and smooth mappings is Cartesian closed. The principal objective in this paper is to show that the full subcategory of Frolicher spaces that believe in fantasy that every Weil functor is really an exponentiation by the corresponding infinitesimal object is also Cartesian closed. Under the assumption that a conjecture holds, it is shown that these Frolicher spaces embed into the Cahier topos with the Cartesian closed structure being preserved.