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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeMar 30th 2011
   • (edited May 12th 2013)
   • PermaLink
   Author: Urs
   Format: MarkdownItexThere used to be a warning at [[infinity-Lie algebra cohomology]] about whether or not a certain functor needs to be regarded as a derived functor in order to get the correct homotopy-theoretic interpretation of oo-Lie algebroid extensions. I think I have now spelled out at [[synthetic differential infinity-groupoid]] the required details and so I replaced that warning with a pointer to a section in that latter entry. All this can do with a good bit more polishing. I'll see what I can do eventually.

   There used to be a warning at infinity-Lie algebra cohomology about whether or not a certain functor needs to be regarded as a derived functor in order to get the correct homotopy-theoretic interpretation of oo-Lie algebroid extensions. I think I have now spelled out at synthetic differential infinity-groupoid the required details and so I replaced that warning with a pointer to a section in that latter entry.

   All this can do with a good bit more polishing. I’ll see what I can do eventually.

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeMay 12th 2013
   • PermaLink
   Author: Urs
   Format: MarkdownItexHave added pointers to the recognition theorem for homotopy fibers of $L_\infty$-homomorphisms -- hence for $L_\infty$-algebra extensions classified by $L_\infty$-cocycles -- which is theorem 3.1.13 in [Fiorenza-Rogers-Schreiber 13](http://arxiv.org/abs/1304.6292) to * _[[infinity-Lie algebra cohomology]]_ * _[string Lie 2-algebra -- As a homotopy fiber](http://ncatlab.org/nlab/show/String+Lie+2-algebra#AsHomotopyFiber)_ * _[model structure for L-infinity algebras -- Properties -- Homotopy fiber products](http://ncatlab.org/nlab/show/model%20structure%20for%20L-infinity%20algebras#HomotopyFiberProducts)_

   Have added pointers to the recognition theorem for homotopy fibers of $L_\infty$-homomorphisms – hence for $L_\infty$-algebra extensions classified by $L_\infty$-cocycles – which is theorem 3.1.13 in Fiorenza-Rogers-Schreiber 13 to

   • infinity-Lie algebra cohomology

   • string Lie 2-algebra – As a homotopy fiber

   • model structure for L-infinity algebras – Properties – Homotopy fiber products