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A Prop Structure on Partitions

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  • Additional Information
    • Contributors:
      Laboratoire Analyse, Géométrie et Applications (LAGA); Université Paris 8 Vincennes-Saint-Denis (UP8)-Centre National de la Recherche Scientifique (CNRS)-Université Sorbonne Paris Nord; École normale supérieure - Paris (ENS-PSL); Université Paris Sciences et Lettres (PSL); Kalamazoo College; Institut de Mathématiques de Jussieu - Paris Rive Gauche (IMJ-PRG (UMR_7586)); Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité); Institut de Mathématiques de Marseille (I2M); Aix Marseille Université (AMU)-École Centrale de Marseille (ECM)-Centre National de la Recherche Scientifique (CNRS); Department of Mathematics Cornell; Cornell University New York
    • Publication Information:
      HAL CCSD
    • Publication Date:
      2024
    • Collection:
      Université Paris 8 Vincennes-Saint-Denis: HAL
    • Abstract:
      Motivated by its link with functor homology, we study the prop freely generated by the operadic suspension of the operad Com. We exhibit a particular family of generators, for which the composition and the symmetric group actions admit simple descriptions. We highlight associated subcategories of its Karoubi envelope which allows us to compute extensions groups between simple functors from free groups. We construct a particular prop structure on partitions whose composition corresponds to the Yoneda product of extensions between exterior power functors.
    • Relation:
      info:eu-repo/semantics/altIdentifier/arxiv/2402.12895; hal-04465168; https://hal.science/hal-04465168; https://hal.science/hal-04465168/document; https://hal.science/hal-04465168/file/EHLVZ-WIT.pdf; ARXIV: 2402.12895
    • Online Access:
      https://hal.science/hal-04465168
      https://hal.science/hal-04465168/document
      https://hal.science/hal-04465168/file/EHLVZ-WIT.pdf
    • Rights:
      info:eu-repo/semantics/OpenAccess
    • Accession Number:
      edsbas.6420D2C6