Beyond the Regnant Philosophy of Manifolds

Abstract

Frolicher spaces and smooth mappings form a cartesian closed category. It was shown in our previous paper [Far East Journal of Mathematical Sciences, 35 (2009), 211-233] that its full subcategory of Weil exponentiable Frolicher spaces is cartesian closed. By emancipating microlinearity from within a well-adapted model of synthetic differential geometry to Frolicher spaces, we get the notion of microlinearity for Frolicher spaces. It is shown in this paper that its full subcategory of Weil exponentiable and microlinear Frolicher spaces is cartesian closed. The canonical embedding of Weil exponentiable Frolicher spaces into the Cahiers topos is shown to preserve microlinearity.