Displaying similar documents to “Universal connections on Lie groupoids.”

Functorial prolongations of Lie groupoids

Ivan Kolář (2007)

Banach Center Publications

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For every Lie groupoid Φ with m-dimensional base M and every fiber product preserving bundle functor F on the category of fibered manifolds with m-dimensional bases and fiber preserving maps with local diffeomorphisms as base maps, we construct a Lie groupoid ℱ Φ over M. Every action of Φ on a fibered manifold Y → M is extended to an action of ℱ Φ on FY → M.

Principal bundles, groupoids, and connections

Anders Kock (2007)

Banach Center Publications

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We clarify in which precise sense the theory of principal bundles and the theory of groupoids are equivalent; and how this equivalence of theories, in the differentiable case, reflects itself in the theory of connections. The method used is that of synthetic differential geometry.