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:
“Nature herself has not provided the most graceful end for her creatures. What becomes of all these birds that people the air and forest for our solacement? The sparrow seems always chipper, never infirm. We do not see their bodies lie about. Yet there is a tragedy at the end of each one of their lives. They must perish miserably; not one of them is translated. True, “not a sparrow falleth to the ground without our Heavenly Father’s knowledge,” but they do fall, nevertheless.”
—Henry David Thoreau (1817–1862)