Smooth spaces: convenient categories for differential geometry

From CRCG-Wiki

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.

Here are slides (in progress) for my talk:

• Smooth Spaces: Convenient Categories for Differential Geometry. 11 am-12 pm, Thursday February 5th.

For more details, see:

• John Baez and Alexander Hoffnung, Convenient Categories of Smooth Spaces

Also see my website.