Frobenius and commutative pseudomonoids in the bicategory of spans

buir.contributor.authorStern, Walker H.
buir.contributor.orcid0000-0002-3800-3528
dc.citation.epage105309-31
dc.citation.spage105309-1
dc.citation.volumeNumber207
dc.contributor.authorContreras, I.
dc.contributor.authorMehta, R. A.
dc.contributor.authorStern, Walker H.
dc.date.accessioned2025-02-15T14:43:12Z
dc.date.available2025-02-15T14:43:12Z
dc.date.issued2024-09-04
dc.departmentDepartment of Mathematics
dc.description.abstractIn previous work by the first two authors, Frobenius and commutative algebra objects in the category of spans of sets were characterized in terms of simplicial sets satisfying certain properties. In this paper, we find a similar characterization for the analogous coherent structures in the bicategory of spans of sets. We show that commutative and Frobenius pseudomonoids in Span correspond, respectively, to paracyclic sets and - sets satisfying the 2-Segal conditions. These results connect closely with work of the third author on A∞ algebras in ∞-categories of spans, as well as the growing body of work on higher Segal objects. Because our motivation comes from symplectic geometry and topological field theory, we emphasize the direct and computational nature of the classifications and their proofs.
dc.description.provenanceSubmitted by Mervenur Sarıgül (mervenur.sarigul@bilkent.edu.tr) on 2025-02-15T14:43:12Z No. of bitstreams: 1 Frobenius_and_commutative_pseudomonoids_in_the_bicategory_of_spans.pdf: 751085 bytes, checksum: f026ae14d1f4609516c3873153550d3a (MD5)en
dc.description.provenanceMade available in DSpace on 2025-02-15T14:43:12Z (GMT). No. of bitstreams: 1 Frobenius_and_commutative_pseudomonoids_in_the_bicategory_of_spans.pdf: 751085 bytes, checksum: f026ae14d1f4609516c3873153550d3a (MD5) Previous issue date: 2024-09-04en
dc.embargo.release2026-09-04
dc.identifier.doi10.1016/j.geomphys.2024.105309
dc.identifier.eissn1879-1662
dc.identifier.issn0393-0440
dc.identifier.urihttps://hdl.handle.net/11693/116275
dc.language.isoEnglish
dc.publisherElsevier BV * North-Holland
dc.relation.isversionofhttps://dx.doi.org/10.1016/j.geomphys.2024.105309
dc.rightsCC BY 4.0 (Attribution 4.0 International Deed)
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.source.titleJournal of Geometry and Physics
dc.subjectSpans
dc.subjectTopological quantum field theory
dc.subject2-categories
dc.subject2-Segal objects
dc.subjectFrobenius algebras
dc.subjectCommutative algebras
dc.titleFrobenius and commutative pseudomonoids in the bicategory of spans
dc.typeArticle

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