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

]]>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.

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