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Connected Lie Groupoids are Internally Connected and Integral Complete in Synthetic Differential Geometry
Symmetry, integrability and geometry: methods and applications, Tome 13 (2017) Cet article a éte moissonné depuis la source Math-Net.Ru

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We extend some fundamental definitions and constructions in the established generalisation of Lie theory involving Lie groupoids by reformulating them in terms of groupoids internal to a well-adapted model of synthetic differential geometry. In particular we define internal counterparts of the definitions of source path and source simply connected groupoid and the integration of $A$-paths. The main results of this paper show that if a classical Hausdorff Lie groupoid satisfies one of the classical connectedness conditions it also satisfies its internal counterpart.
Keywords: Lie theory; Lie groupoid; Lie algebroid; category theory; synthetic differential geometry; intuitionistic logic. 
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     author = {Matthew Burke},
     title = {Connected {Lie} {Groupoids} are {Internally} {Connected} and {Integral} {Complete} in {Synthetic} {Differential} {Geometry}},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2017_13_a6/}
}
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Matthew Burke. Connected Lie Groupoids are Internally Connected and Integral Complete in Synthetic Differential Geometry. Symmetry, integrability and geometry: methods and applications, Tome 13 (2017). http://geodesic.mathdoc.fr/item/SIGMA_2017_13_a6/

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