Contents -- Preface -- Organizing Committees -- Speakers and Lectures -- Participants and Photos -- Grobner-Shirshov Bases for Categories L. A. Bokut, Yuqun Chen and Yu Li -- 1. Introduction -- 2. A short survey on Grobner-Shirshov bases -- 3. Composition-Diamond lemma for categories -- 3.1. Free categories and category partial algebras -- 3.2. Composition-Diamond lemma for category partial algebras -- 4. Grobner-Shirshov bases for the simplicial category and the cyclic category -- 4.1. Grobner-Shirshov basis for the simplicial category -- 4.2. Grobner-Shirshov basis for the cyclic category -- References -- Operads, Clones, and Distributive Laws Pierre-Louis Curien -- 1. Introduction -- 2. Three useful combinators -- 3. Kan extensions -- 4. Kelly's account of operads -- 5. Operads from analytic functors -- 6. Profunctors -- 7. Profunctors as a Kleisli category -- 8. Distributive laws -- 9. A !/Psh distributive law -- 10. Intermezzo -- 11. The (bi)category Prof ? -- 12. Cooperads and properads -- References -- Leibniz Superalgebras Graded by Finite Root Systems Naihong Hu, Dong Liu and Linsheng Zhu -- 1. Introduction -- 2. Associative super dialgebras and leibniz superalgebras -- 2.1. Associative super dialgebras -- 2.2. Leibniz superalgebra -- 2.3. Leibniz algebras graded by finite root systems -- 3. Leibniz superalgebras graded by finite root systems -- 4. The structure of the A(m, n)-graded Leibniz superalgebras (m > n) -- 5. The structure of -graded Leibniz superalgebras of other types -- ACKNOWLEDGMENTS -- References -- Tridendriform Algebras Spanned by Partitions Daniel Jimenez and Marıa Ronco -- Introduction -- 1. Preliminaries -- Shuffles -- 2. Rota-Baxter algebras and tridendriform bialgebras -- 3. Tridendriform structure on the space of partitions -- 4. Tridendriform algebra structure on the maps between finite sets -- References.

Generalized Disjunctive Languages and Universal Algebra Yun Liu -- 1. Introduction -- 2. K-Disjunctive languages and universal algebra -- 3. Generalized disjunctive hierarchy -- Acknowledgements -- References -- Koszul Duality of the Category of Trees and Bar Constructions for Operads Muriel Livernet -- Introduction -- 1. The tree category is Koszul -- 1.1. The tree category TI -- 1.2. Bar construction for the category TI -- 1.2.1. Bar construction -- 1.2.2. Resolution of left and right TI -modules and Tor functors -- 1.2.3. Normalized bar complex -- 1.3. The Koszul complex of the category TI -- 1.3.1. The Koszul complex -- 1.3.2. The Koszul complex of the category TI with coefficients -- 1.4. The category TI is Koszul -- 1.5. Bibliographical remarks -- 2. Comparison of three di erent types of bar constructions for an operad -- 2.1. Principle of the bar construction with coefficients -- 2.2. Operads as left TI-modules -- 2.3. Two-sided bar construction from the free operad functor -- 2.3.1. The two-sided bar construction -- 2.3.2. Right TI -modules and F-functors -- 2.4. The bar construction with respect to the monoidal structure -- 2.5. The classical bar construction of operads, and the levelization morphism -- 2.6. The factorization of : K(bI , TI ,P) . N(bI , TI ,P) -- 3. Resolution of the category TI and operads up to homotopy -- 3.1. Bar and cobar constructions for dg categories and dg cocategories -- 3.2. Minimal model of the category TI -- 3.3. Operads up to homotopy -- Acknowledgments -- References -- Some Problems in Operad Theory Jean-Louis Loday -- Introduction -- 1. On the notion of group up to homotopy -- 2. Subgroup of free group -- 3. The octonions as an algebra over a Koszul operad -- 4. Commutative algebras up to homotopy in positive characteristic -- 5. Manin black product for operads.

6. L-dendriform algebras and operadic black product -- 7. Resolutions of associative algebras -- 8. Hidden structure for EZ-AW maps -- 9. Interpolating between Dend and Com -- 10. Good triples of binary quadratic operads -- 11. On the coalgebra structure of Connes-Kreimer Hopf algebra -- 12. Generalized bialgebras in positive characteristic -- 13. Higher Dynkin diagrams and operads -- 14. Coquecigrues -- 15. Homotopy groups of spheres -- References -- Hom-dendriform Algebras and Rota-Baxter Hom-algebras Abdenacer Makhlouf -- Introduction -- 1. Hom-associative, Hom-Lie and Hom-preLie algebras -- 1.1. Hom-associative algebras -- 1.2. Hom-Lie algebras -- 1.3. Hom-preLie algebras -- 2. Hom-dendriform algebras and Hom-Tridendriform algebras -- 2.1. Hom-dendriform algebras -- 2.2. Hom-tridendriform algebras -- 3. Rota-Baxter operators and Hom-associative algebras -- 4. Some functors -- 5. Rota-Baxter operators and Hom-Nonassociative algebras -- Acknowledgments -- References -- Free Field Realizations of the Current Algebras Associated with (Super) Lie Algebras Wen-Li Yang -- 1. Introduction -- 2. Notation and preliminaries -- 3. Differential operator realizations of superalgebras -- 3.1. Differential operator realization of gl(r

3.1. Free TD algebra on a module as decorated forests -- 3.2. Free TD algebra on a set -- 4. Construction of free TD algebras by Motzkin paths -- 4.1. Review of the Motzkin path -- 4.2. Free TD algebras in terms of Motzkin paths -- References -- Encyclopedia of Types of Algebras 2010 G. W. Zinbiel -- Introduction -- 1. Type of algebras -- References -- Author Index.