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    • CommentRowNumber1.
    • CommentAuthorDmitri Pavlov
    • CommentTimeFeb 15th 2023

    Created:

    Definition

    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.

    Related concepts

    References

    v1, current

    • CommentRowNumber2.
    • CommentAuthorDavidRoberts
    • CommentTimeFeb 15th 2023

    Added the reference to Ehresmann’s 1959 paper

    diff, v2, current

    • CommentRowNumber3.
    • CommentAuthorDavidRoberts
    • CommentTimeFeb 15th 2023

    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.

    • CommentRowNumber4.
    • CommentAuthorJoe Moeller
    • CommentTimeSep 10th 2024

    added link to Lie monoid

    diff, v3, current