Convenient Categories of Smooth Spaces

@article{Baez2008ConvenientCO,
  title={Convenient Categories of Smooth Spaces},
  author={John C. Baez and Alexander E. Hoffnung},
  journal={arXiv: Differential Geometry},
  year={2008}
}
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… 
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