Comparative Smootheology

By Andrew Stacey. Theory and Applications of Categories, 2008

65 citations recorded by the source corpus.

We compare various different definitions of"the category of smooth objects". The definitions compared are due to Chen, Fr\"olicher, Sikorski, Smith, and Souriau. The method of comparison is to construct functors between the categories that enable us to see how the categories relate to each other. This produces a diagram of categories with the category of Fr\"olicher spaces sitting at its centre. Our method of study involves finding a general context into which these categories can be placed. This involves considering categories wherein objects are considered in relation to a certain collection of standard test objects. This therefore applies beyond the question of categories of smooth spaces.

Subfields: Geometry and Topology, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/ee2a2a902c126a0db3f3459189b6b1843324d48c

Citations in the corpus

• The D-topology for diffeological spaces (2013, unknown): “Since the 1970s, the category of smooth manifolds has been enlarged in several different ways to a well-behaved category as described above, and these approaches are nicely summarized and compared in [Stacey 2011].”