LEADER 05482nam 2200697 a 450 001 9910823329403321 005 20240516164234.0 010 $a1-280-66960-8 010 $a9786613646538 010 $a981-4365-12-2 035 $a(CKB)2550000000101624 035 $a(EBL)919093 035 $a(OCoLC)794328388 035 $a(SSID)ssj0001013052 035 $a(PQKBManifestationID)11567592 035 $a(PQKBTitleCode)TC0001013052 035 $a(PQKBWorkID)11056538 035 $a(PQKB)10538774 035 $a(MiAaPQ)EBC919093 035 $a(WSP)00002669 035 $a(Au-PeEL)EBL919093 035 $a(CaPaEBR)ebr10563480 035 $a(CaONFJC)MIL364653 035 $a(EXLCZ)992550000000101624 100 $a20120611d2012 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aOperads and universal algebra $eproceedings of the International Conference on Operads and Universal Algebra, Tianjin, China, 5-9 July 2010 /$fedited by Chengming Bai, Li Guo, Jean-Louis Loday 205 $a1st ed. 210 $aSingapore $cWorld Scientific Pub. Co.$d2012 215 $a1 online resource (318 p.) 225 1 $aNankai series in pure, applied mathematics and theoretical physics ;$vv. 9 300 $aDescription based upon print version of record. 311 $a981-4365-11-4 320 $aIncludes bibliographical references and indexes. 327 $aPreface; 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 327 $aOperads, 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 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 327 $a2.2. 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 Mar?a 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 327 $aReferencesGeneralized 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 327 $a1.3.1. 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 327 $a2.5. The classical bar construction of operads, and the levelization morphism 330 $aThe book aims to exemplify the recent developments in operad theory, in universal algebra and related topics in algebraic topology and theoretical physics. The conference has established a better connection between mathematicians working on operads (mainly the French team) and mathematicians working in universal algebra (primarily the Chinese team), and to exchange problems, methods and techniques from these two subject areas. 410 0$aNankai series in pure, applied mathematics and theoretical physics ;$vv. 9. 606 $aOperads$vCongresses 606 $aAlgebra, Universal$vCongresses 615 0$aOperads 615 0$aAlgebra, Universal 676 $a512.62 701 $aBai$b Chengming$01626675 701 $aGuo$b Li$0611852 701 $aLoday$b Jean-Louis$057212 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910823329403321 996 $aOperads and universal algebra$94083030 997 $aUNINA