FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W643620113> ?p ?o ?g. }

• W643620113 abstract "This research monograph integrates ideas from category theory, algebra and combinatorics. It is organised in three parts. Part I belongs to the realm of category theory. It reviews some of the foundational work of Benabou, Eilenberg, Kelly and Mac Lane on monoidal categories and of Joyal and Street on braided monoidal categories, and proceeds to study higher monoidal categories and higher monoidal functors. Special attention is devoted to the notion of a bilax monoidal functor which plays a central role in this work. Combinatorics and geometry are the theme of Part II. Joyal's species constitute a good framework for the study of algebraic structures associated to combinatorial objects. This part discusses the category of species focusing particularly on the Hopf monoids therein. The notion of a Hopf monoid in species parallels that of a Hopf algebra and reflects the manner in which combinatorial structures compose and decompose. Numerous examples of Hopf monoids are given in the text. These are constructed from combinatorial and geometric data and inspired by ideas of Rota and Tits' theory of Coxeter complexes. Part III is of an algebraic nature and shows how ideas in Parts I and II lead to a unified approach to Hopf algebras. The main step is the construction of Fock functors from species to graded vector spaces. These functors are bilax monoidal and thus translate Hopf monoids in species to graded Hopf algebras. This functorial construction of Hopf algebras encompasses both quantum groups and the Hopf algebras of recent prominence in the combinatorics literature. The monograph opens a vast new area of research. It is written with clarity and sufficient detail to make it accessible to advanced graduate students. Titles in this series are co-published with the Centre de Recherches Mathematiques.|This research monograph integrates ideas from category theory, algebra and combinatorics. It is organised in three parts. Part I belongs to the realm of category theory. It reviews some of the foundational work of Benabou, Eilenberg, Kelly and Mac Lane on monoidal categories and of Joyal and Street on braided monoidal categories, and proceeds to study higher monoidal categories and higher monoidal functors. Special attention is devoted to the notion of a bilax monoidal functor which plays a central role in this work. Combinatorics and geometry are the theme of Part II. Joyal's species constitute a good framework for the study of algebraic structures associated to combinatorial objects. This part discusses the category of species focusing particularly on the Hopf monoids therein. The notion of a Hopf monoid in species parallels that of a Hopf algebra and reflects the manner in which combinatorial structures compose and decompose. Numerous examples of Hopf monoids are given in the text. These are constructed from combinatorial and geometric data and inspired by ideas of Rota and Tits' theory of Coxeter complexes. Part III is of an algebraic nature and shows how ideas in Parts I and II lead to a unified approach to Hopf algebras. The main step is the construction of Fock functors from species to graded vector spaces. These functors are bilax monoidal and thus translate Hopf monoids in species to graded Hopf algebras. This functorial construction of Hopf algebras encompasses both quantum groups and the Hopf algebras of recent prominence in the combinatorics literature. The monograph opens a vast new area of research. It is written with clarity and sufficient detail to make it accessible to advanced graduate students. Titles in this series are co-published with the Centre de Recherches Mathematiques." @default.
• W643620113 created "2016-06-24" @default.
• W643620113 creator A5002881372 @default.
• W643620113 creator A5060744601 @default.
• W643620113 date "2010-10-20" @default.
• W643620113 modified "2023-10-18" @default.
• W643620113 title "Monoidal Functors, Species and Hopf Algebras" @default.
• W643620113 doi "https://doi.org/10.1090/crmm/029" @default.
• W643620113 hasPublicationYear "2010" @default.
• W643620113 type Work @default.
• W643620113 sameAs 643620113 @default.
• W643620113 citedByCount "211" @default.
• W643620113 countsByYear W6436201132012 @default.
• W643620113 countsByYear W6436201132013 @default.
• W643620113 countsByYear W6436201132014 @default.
• W643620113 countsByYear W6436201132015 @default.
• W643620113 countsByYear W6436201132016 @default.
• W643620113 countsByYear W6436201132017 @default.
• W643620113 countsByYear W6436201132018 @default.
• W643620113 countsByYear W6436201132019 @default.
• W643620113 countsByYear W6436201132020 @default.
• W643620113 countsByYear W6436201132021 @default.
• W643620113 countsByYear W6436201132022 @default.
• W643620113 countsByYear W6436201132023 @default.
• W643620113 crossrefType "monograph" @default.
• W643620113 hasAuthorship W643620113A5002881372 @default.
• W643620113 hasAuthorship W643620113A5060744601 @default.
• W643620113 hasConcept C136119220 @default.
• W643620113 hasConcept C156772000 @default.
• W643620113 hasConcept C202444582 @default.
• W643620113 hasConcept C29712632 @default.
• W643620113 hasConcept C33923547 @default.
• W643620113 hasConceptScore W643620113C136119220 @default.
• W643620113 hasConceptScore W643620113C156772000 @default.
• W643620113 hasConceptScore W643620113C202444582 @default.
• W643620113 hasConceptScore W643620113C29712632 @default.
• W643620113 hasConceptScore W643620113C33923547 @default.
• W643620113 hasLocation W6436201131 @default.
• W643620113 hasOpenAccess W643620113 @default.
• W643620113 hasPrimaryLocation W6436201131 @default.
• W643620113 hasRelatedWork W1505712091 @default.
• W643620113 hasRelatedWork W1662158574 @default.
• W643620113 hasRelatedWork W1912064545 @default.
• W643620113 hasRelatedWork W2142802962 @default.
• W643620113 hasRelatedWork W2150706552 @default.
• W643620113 hasRelatedWork W2576866533 @default.
• W643620113 hasRelatedWork W2952525972 @default.
• W643620113 hasRelatedWork W2962848624 @default.
• W643620113 hasRelatedWork W4300969443 @default.
• W643620113 hasRelatedWork W187450818 @default.
• W643620113 isParatext "false" @default.
• W643620113 isRetracted "false" @default.
• W643620113 magId "643620113" @default.
• W643620113 workType "book" @default.