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1. • CommentRowNumber1.
   • CommentAuthorfgyamauti
   • CommentTimeOct 2nd 2015
   • (edited Oct 2nd 2015)
   • PermaLink
   Author: fgyamauti
   Format: MarkdownItexHi, do someone have patience to explain how is the Lie differentiation of $\infty$-Lie groupoids? More precisely, I'm assuming that a $\infty$-Lie groupoid is a simplicial manifold satisfying the usual Kan fibrancy assumption (the restriction from n-simplices to the i-th horn is a surjective submersion) as in [http://arxiv.org/abs/math/0603563](http://arxiv.org/abs/math/0603563) . However [in nlab](http://ncatlab.org/nlab/show/formal+smooth+infinity-groupoid#LieDifferentiation), as I understand, it's assumed a more general case in the cohesive synthetic setting (which I know almost nothing about and apparently is not so explicit) using infinitesimally thickened simplexes. Is there a more explicit construction that differentiate a Lie groupoid (in the sense described above) to an [$\infty$-Lie algebroid](http://ncatlab.org/nlab/show/Lie+infinity-algebroid)? Maybe an illustrative example would be how to make this construction using the nerve of an ordinary Lie groupoid to obtain the usual Lie algebroid (as a cochain complex concentrated in degreee 1). Thanks in advance.

   Hi, do someone have patience to explain how is the Lie differentiation of $\infty$-Lie groupoids? More precisely, I’m assuming that a $\infty$-Lie groupoid is a simplicial manifold satisfying the usual Kan fibrancy assumption (the restriction from n-simplices to the i-th horn is a surjective submersion) as in http://arxiv.org/abs/math/0603563 . However in nlab, as I understand, it’s assumed a more general case in the cohesive synthetic setting (which I know almost nothing about and apparently is not so explicit) using infinitesimally thickened simplexes. Is there a more explicit construction that differentiate a Lie groupoid (in the sense described above) to an $\infty$-Lie algebroid? Maybe an illustrative example would be how to make this construction using the nerve of an ordinary Lie groupoid to obtain the usual Lie algebroid (as a cochain complex concentrated in degreee 1).

   Thanks in advance.