Explore: Lie Groupoids

correspondence between Lie groups and Lie algebras, Lie groupoids are the global counterparts of Lie algebroids. Lie groupoids were introduced by Charles

of Lie groupoids that Lie algebras play in the theory of Lie groups: reducing global problems to infinitesimal ones. Indeed, any Lie groupoid gives rise

proper groupoids are automatically compact, the discreteness condition implies that the isotropies must be actually finite groups. Orbifold groupoids play

usually not employed in symplectic geometry, such as the theory of Lie groupoids and algebroids. Moreover, there are natural examples of structures which

arising groupoids often carry a topology, turning them into topological groupoids, or even some differentiable structure, turning them into Lie groupoids. These

prominent author on the subject of groupoids in topology: http://groupoids.org.uk/ fundamental groupoid at the nLab fundamental infinity-groupoid at the nLab

of a Lie group to Lie supergroups. This categorical point of view leads also to a different generalization of Lie groups, namely Lie groupoids, which

generalising Lie bialgebroids Lie algebroid, the infinitesimal counterpart of Lie groupoids Atiyah algebroid, a fundamental example of a Lie algebroid associated

orbifolds are viewed as differentiable stacks presented by étale proper Lie groupoids, then there is a functor from the underlying 1-category of orbifolds

geometry and twisted K-theory. Recall that a category fibred in groupoids (also called a groupoid fibration) consists of a category C {\displaystyle {\mathcal