In mathematics, a Lie groupoid is a groupoid where the set of objects and the set of morphisms are both manifolds, the source and target operations
are submersions, and all the category operations (source and target, composition, and identity-assigning map) are smooth.
A Lie groupoid can thus be thought of as a "many-object generalization" of a Lie group, just as a groupoid is a many-object generalization of a group. Just as every Lie group has a Lie algebra, every Lie groupoid has a Lie algebroid.
Read more about Lie Groupoid: Examples, Morita Morphisms and Smooth Stacks
Famous quotes containing the word lie:
“All morality depends upon our sentiments; and when any action or quality of the mind pleases us after a certain manner we say it is virtuous; and when the neglect or nonperformance of it displeases us after a like manner, we say that we lie under an obligation to perform it.”
—David Hume (1711–1776)