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Smooth spaces: convenient categories for differential geometry
by
Alexander Hoffnung
University of California, Riverside
Coauthors: John Baez
In 1977 K.T. Chen introduced a notion of smooth spaces as a generalization of the category of smooth manifolds. In 1979 Souriau introduced another notion, 'diffeological spaces', serving the same purposes. Both of these categories have all limits and colimits, and are cartesian closed. In fact, following ideas of Dubuc, we give a unified proof that the categories of Chen spaces, diffeological spaces, and simplicial complexes are 'quasitopoi': locally cartesian closed categories with finite (and in these cases all) colimits and a weak subobject classifier.
Date received: March 18, 2008
Copyright © 2008 by the author(s). The author(s) of this work and the organizers of the conference have granted their consent to include this abstract in Topology Atlas. Document # cawt-10.