  We show that there is a fully faithful embedding of the category of manifolds
with corners into the Cahiers topos, one of the premier models for Synthetic
Differential Geometry. This embedding is shown to have a number of nice
properties, such as preservation of open covers and transverse fibre products.
  We develop a theory for gluing manifolds with corners in the Cahiers topos.
In this setting, the result of gluing together manifolds with corners along a
common face is shown to coincide with a pushout along an infinitesimally
thickened face. Our theory is designed with a view toward future applications
in Field Theory within the context of Synthetic Differential Geometry.
