Convenient Categories of Smooth Spaces

Mathematics – Differential Geometry

Scientific paper

Rate now

  [ 0.00 ] – not rated yet Voters 0   Comments 0

Details

43 pages, version to be published; includes corrected definition of "concrete site"

Scientific paper

A "Chen space" is a set X equipped with a collection of "plots" - maps from convex sets to X - satisfying three simple axioms. While an individual Chen space can be much worse than a smooth manifold, the category of all Chen spaces is much better behaved than the category of smooth manifolds. For example, any subspace or quotient space of a Chen space is a Chen space, and the space of smooth maps between Chen spaces is again a Chen space. Souriau's "diffeological spaces" share these convenient properties. Here we give a unified treatment of both formalisms. Following ideas of Dubuc, we show that Chen spaces, diffeological spaces, and even simplicial complexes are examples of "concrete sheaves on a concrete site". As a result, the categories of such spaces are locally cartesian closed, with all limits, all colimits, and a weak subobject classifier. For the benefit of differential geometers, our treatment explains most of the category theory we use.

No associations

LandOfFree

Say what you really think

Search LandOfFree.com for scientists and scientific papers. Rate them and share your experience with other people.

Rating

Convenient Categories of Smooth Spaces does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Convenient Categories of Smooth Spaces, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Convenient Categories of Smooth Spaces will most certainly appreciate the feedback.

Rate now

     

Profile ID: LFWR-SCP-O-460132

  Search
All data on this website is collected from public sources. Our data reflects the most accurate information available at the time of publication.