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Record Nr. |
UNINA9910779285303321 |
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Titolo |
Operads and universal algebra [[electronic resource] ] : proceedings of the International Conference on Operads and Universal Algebra, Tianjin, China, 5-9 July 2010 / / edited by Chengming Bai, Li Guo, Jean-Louis Loday |
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Pubbl/distr/stampa |
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Singapore, : World Scientific Pub. Co., 2012 |
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ISBN |
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1-280-66960-8 |
9786613646538 |
981-4365-12-2 |
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Descrizione fisica |
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1 online resource (318 p.) |
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Collana |
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Nankai series in pure, applied mathematics and theoretical physics ; ; v. 9 |
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Altri autori (Persone) |
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BaiChengming |
GuoLi |
LodayJean-Louis |
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Disciplina |
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Soggetti |
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Operads |
Algebra, Universal |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Description based upon print version of record. |
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Nota di bibliografia |
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Includes bibliographical references and indexes. |
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Nota di contenuto |
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Preface; Organizing Committees; Speakers and Lectures; Participants and Photos; Contents; 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 Curien1. 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 |
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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 superalgebra2.3. 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 |
ReferencesGeneralized 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 complex1.3.2. 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 |
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Sommario/riassunto |
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The book aims to exemplify the recent developments in operad theory, in universal algebra and related topics in algebraic topology and theoretical physics. The conference has established a better connection between mathematicians working on operads (mainly the French team) and mathematicians working in universal algebra (primarily the Chinese team), and to exchange problems, methods and techniques from these two subject areas. |
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