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Pré-Publication, Document De Travail Année : 2024

A Prop Structure on Partitions

Résumé

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.
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Dates et versions

hal-04465168 , version 1 (19-02-2024)

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Coline Emprin, Dana Hunter, Muriel Livernet, Christine Vespa, Inna Zakharevich. A Prop Structure on Partitions. 2024. ⟨hal-04465168⟩
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