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G.E. Reyes, Embedding manifolds with boundary in smooth toposes, Cahiers de Top. et Geom. Diff. Catég., (48), 83-103, (2007). We embed fully and faithfully the category of manifolds with boundary in some “smooth” toposes. We show that the embedding preserves open coverings and some products. Furthermore, it sends a Weil’s prolongation of a manifold by a Weil algebra into the embedded manifold raised to the associated infinitesimal space of the algebra. Our main tool is to “double” the manifold with boundary to obtain one without boundary.
Gonzalo E. Reyes - Marie La Palme Reyes 