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2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry book bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics complex complex-geometry computable-mathematics computer-science constructive cosmology definitions deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration foundation foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nforum nlab noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pages pasting philosophy physics pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes set set-theory sheaf simplicial space spin-geometry stable-homotopy-theory stack string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft type type-theory universal variational-calculus

1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeAug 8th 2011
   • PermaLink
   Author: Urs
   Format: MarkdownItexam starting an entry [[simplicial Lie algebra]]

   am starting an entry simplicial Lie algebra

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeAug 8th 2011
   • PermaLink
   Author: Urs
   Format: MarkdownItexI have added some central statements by Quillen on the equivalence to dg-Lie algebras. Still very imperfect, but need to quit now for tonight.

   I have added some central statements by Quillen on the equivalence to dg-Lie algebras. Still very imperfect, but need to quit now for tonight.

3. • CommentRowNumber3.
   • CommentAuthorzskoda
   • CommentTimeAug 8th 2011
   • (edited Aug 8th 2011)
   • PermaLink
   Author: zskoda
   Format: MarkdownItexProbably this works only for Lie algebras over a ground ring $k$ of [[characteristic zero]] like the analogous fact for (simplicial vs dg) commutative unital $k$-algebras, which is the fact about the Koszul dual operad.

   Probably this works only for Lie algebras over a ground ring $k$ of characteristic zero like the analogous fact for (simplicial vs dg) commutative unital $k$-algebras, which is the fact about the Koszul dual operad.

4. • CommentRowNumber4.
   • CommentAuthorUrs
   • CommentTimeAug 8th 2011
   • (edited Aug 8th 2011)
   • PermaLink
   Author: Urs
   Format: MarkdownItexYes, sorry, that's on p. 219 of Quillen's article. I have now fixed this in the entry.

   Yes, sorry, that’s on p. 219 of Quillen’s article. I have now fixed this in the entry.