An internal category object in the category of smooth manifolds in which the source and target maps are submersions.

Sometimes, the smooth manifold of morphisms is allowed to have a boundary, in which case the restrictions of the source and target maps to the boundary are required to be submersions themselves.

The notion of Lie category goes back to

- Charles Ehresmann,
*Catégories topologiques et categories différentiables*, Colloque de Géométrie différentielle globale, Bruxelles, C.B.R.M., (1959) pp. 137-150 (pdf, zbMath:0205.28202)

which also allowed for $C^r$ manifolds and structure maps.

A more recent study, including the case involving manifolds with boundary, is

- Žan Grad,
*Fundamentals of Lie categories*, arXiv:2302.05233.

Last revised on February 15, 2023 at 03:49:04. See the history of this page for a list of all contributions to it.