Higher dimensional algebra. VII: Groupoidification.
Baez, John C., Hoffnung, Alexander E., Walker, Christopher D. (2010)
Theory and Applications of Categories [electronic only]
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Baez, John C., Hoffnung, Alexander E., Walker, Christopher D. (2010)
Theory and Applications of Categories [electronic only]
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Starting with some motivating examples (classical atlases for a manifold, space of leaves of a foliation, group orbits), we propose to view a Lie groupoid as a generalized atlas for the “virtual structure” of its orbit space, the equivalence between atlases being here the smooth Morita equivalence. This “structure” keeps memory of the isotropy groups and of the smoothness as well. To take the smoothness into account, we claim that we can go very far by retaining just a few formal properties...
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CONTENTSIntroduction................................................................................................................................................. 3I. TERMS AND NOTATION....................................................................................................................... 5II. GROUPOIDS AND CATEGORIES...................................................................................................... 61. The notion of groupoid............................................................................................................................