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Created:
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.
Ehresmann only required that the source and target maps have locally constant rank, rather than being submersions, IIRC. I’ve not seen any concrete examples that took advantage of this greater generality, though.
added link to Lie monoid
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