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Incidence Bialgebras of Monoidal Categories

Incidence coalgebras of categories as defined by Joni and Rota are studied, specifically in cases where a strict monoidal product on the underlying category turns the incidence coalgebra into a bialgebra or weak bialgebra. Examples of these incidence bialgebras in combinatorics are given, and include rooted trees and forests, skew shapes and bigraphs.
The relations between incidence bialgebras of monoidal categories, incidence bialgebras of operads and posets, combinatorial Hopf algebras and the quiver Hopf algebras of Cibils and Rosso are discussed. Building on a result of Bergbauer and Kreimer, incidence bialgebras are seen as a useful setting in which to study aspects of combinatorial Dyson-Schwinger equations. The possibility of defining a grafting operator B+ and combinatorial DysonSchwinger equations for general incidence bialgebras is explored through the example of skew shapes.:1. Introduction
2. Background
3. Incidence bialgebras of monoidal categories and multicategories
4. Combinatorial Dyson-Schwinger equations

Identiferoai:union.ndltd.org:DRESDEN/oai:qucosa:de:qucosa:74695
Date28 April 2021
CreatorsRotheray, Lucia Alessandra
ContributorsKrähmer, Ulrich, Yeats, Karen, Technische Universität Dresden
Source SetsHochschulschriftenserver (HSSS) der SLUB Dresden
LanguageEnglish
Detected LanguageEnglish
Typeinfo:eu-repo/semantics/publishedVersion, doc-type:doctoralThesis, info:eu-repo/semantics/doctoralThesis, doc-type:Text
Rightsinfo:eu-repo/semantics/openAccess

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