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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 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 internal-categories k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology 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
   • CommentTimeNov 28th 2011
   • PermaLink
   Author: Urs
   Format: MarkdownItexI have added to [[Maurer-Cartan equation]] a brief section [MC elements in L-infinity algebras](http://ncatlab.org/nlab/show/Maurer-Cartan+equation#InLInfinityAlgebras) and then a Properties section [As homomorphisms of L-infinity algebras](http://ncatlab.org/nlab/show/Maurer-Cartan+equation#AsHomomorphisms) where I explain how MC elements are secretly homs of dg/$L_\infty$-algebras.

   I have added to Maurer-Cartan equation a brief section MC elements in L-infinity algebras and then a Properties section As homomorphisms of L-infinity algebras where I explain how MC elements are secretly homs of dg/$L_\infty$-algebras.

2. • CommentRowNumber2.
   • CommentAuthorzskoda
   • CommentTimeNov 28th 2011
   • PermaLink
   Author: zskoda
   Format: MarkdownItexNice, it will be useful for the course I teach :)

   Nice, it will be useful for the course I teach :)

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeAug 12th 2021
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded pointer to: * Joseph Chuang, [[Andrey Lazarev]], *Combinatorics and formal geometry of the master equation*, Lett. Math. Phys. **103** (2013) 79–112 ([arXiv:1205.5970](https://arxiv.org/abs/1205.5970), [doi:10.1007/s11005-012-0586-1](https://doi.org/10.1007/s11005-012-0586-1)) <a href="https://ncatlab.org/nlab/revision/diff/Maurer-Cartan+equation/16">diff</a>, <a href="https://ncatlab.org/nlab/revision/Maurer-Cartan+equation/16">v16</a>, <a href="https://ncatlab.org/nlab/show/Maurer-Cartan+equation">current</a>

   added pointer to:

   • Joseph Chuang, Andrey Lazarev, Combinatorics and formal geometry of the master equation, Lett. Math. Phys. 103 (2013) 79–112 (arXiv:1205.5970, doi:10.1007/s11005-012-0586-1)

   diff, v16, current

4. • CommentRowNumber4.
   • CommentAuthorUrs
   • CommentTimeAug 12th 2021
   • PermaLink
   Author: Urs
   Format: MarkdownItexalso pointer to: * [[Gerd Rudolph]], [[Matthias Schmidt]], Prop. 1.4.9 in: *Differential Geometry and Mathematical Physics Part II. Fibre Bundles, Topology and Gauge Fields*, Springer 2017 ([doi:10.1007/978-94-024-0959-8](https://link.springer.com/book/10.1007/978-94-024-0959-8)) <a href="https://ncatlab.org/nlab/revision/diff/Maurer-Cartan+equation/16">diff</a>, <a href="https://ncatlab.org/nlab/revision/Maurer-Cartan+equation/16">v16</a>, <a href="https://ncatlab.org/nlab/show/Maurer-Cartan+equation">current</a>

   also pointer to:

   • Gerd Rudolph, Matthias Schmidt, Prop. 1.4.9 in: Differential Geometry and Mathematical Physics Part II. Fibre Bundles, Topology and Gauge Fields, Springer 2017 (doi:10.1007/978-94-024-0959-8)

   diff, v16, current

5. • CommentRowNumber5.
   • CommentAuthorUrs
   • CommentTimeAug 12th 2021
   • PermaLink
   Author: Urs
   Format: MarkdownItexand pointer to: * [[Mikio Nakahara]], Section 5.6.4 of: _[[Geometry, Topology and Physics]]_, IOP 2003 ([doi:10.1201/9781315275826](https://doi.org/10.1201/9781315275826), <a href="http://alpha.sinp.msu.ru/~panov/LibBooks/GRAV/(Graduate_Student_Series_in_Physics)Mikio_Nakahara-Geometry,_Topology_and_Physics,_Second_Edition_(Graduate_Student_Series_in_Physics)-Institute_of_Physics_Publishing(2003).pdf">pdf</a>) <a href="https://ncatlab.org/nlab/revision/diff/Maurer-Cartan+equation/16">diff</a>, <a href="https://ncatlab.org/nlab/revision/Maurer-Cartan+equation/16">v16</a>, <a href="https://ncatlab.org/nlab/show/Maurer-Cartan+equation">current</a>

   and pointer to:

   • Mikio Nakahara, Section 5.6.4 of: Geometry, Topology and Physics, IOP 2003 (doi:10.1201/9781315275826, pdf)

   diff, v16, current

6. • CommentRowNumber6.
   • CommentAuthorUrs
   • CommentTimeAug 12th 2021
   • PermaLink
   Author: Urs
   Format: MarkdownItexalso pointer to: * [[Martin Doubek]], [[Martin Markl]], [[Petr Zima]], equation (31) in: *Deformation Theory (lecture notes)*, Archivum mathematicum 43(5), 2007, 333-371 ([arXiv:0705.3719](https://arxiv.org/abs/0705.3719)) <a href="https://ncatlab.org/nlab/revision/diff/Maurer-Cartan+equation/16">diff</a>, <a href="https://ncatlab.org/nlab/revision/Maurer-Cartan+equation/16">v16</a>, <a href="https://ncatlab.org/nlab/show/Maurer-Cartan+equation">current</a>

   also pointer to:

   • Martin Doubek, Martin Markl, Petr Zima, equation (31) in: Deformation Theory (lecture notes), Archivum mathematicum 43(5), 2007, 333-371 (arXiv:0705.3719)

   diff, v16, current

7. • CommentRowNumber7.
   • CommentAuthorUrs
   • CommentTimeAug 12th 2021
   • PermaLink
   Author: Urs
   Format: MarkdownItexalso pointer to: * [[Martin Markl]], Def. 3.11 in: _Deformation theory of algebras and their diagrams_, 129 pp, CBMS __116__, AMS 2012 ([ISBN:978-0-8218-8979-4](http://www.ams.org/bookstore-getitem/item=CBMS-116), [toc pdf](https://www.gbv.de/dms/goettingen/721467989.pdf)) <a href="https://ncatlab.org/nlab/revision/diff/Maurer-Cartan+equation/16">diff</a>, <a href="https://ncatlab.org/nlab/revision/Maurer-Cartan+equation/16">v16</a>, <a href="https://ncatlab.org/nlab/show/Maurer-Cartan+equation">current</a>

   also pointer to:

   • Martin Markl, Def. 3.11 in: Deformation theory of algebras and their diagrams, 129 pp, CBMS 116, AMS 2012 (ISBN:978-0-8218-8979-4, toc pdf)

   diff, v16, current