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:
“Through throats where many rivers meet, the curlews cry,
Under the conceiving moon, on the high chalk hill,
And there this night I walk in the white giant’s thigh
Where barrren as boulders women lie longing still
To labour and love though they lay down long ago.”
—Dylan Thomas (1914–1953)