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A prop structure on partitions
Published 20 Feb 2024 in math.AT | (2402.12895v1)
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.
- Aurélien Djament. Décomposition de hodge pour l’homologie stable des groupes d’automorphismes des groupes libres. Compos. Math., 155(9):1794–1844, 2019.
- V. Drinfeld. Hamiltonian structures on lie groups, lie bialgebras and the geometric meaning of classical yang-baxter equations. Soviet Math. Dokl., 27(1):68–71, 1983.
- V. Drinfeld. Quantum groups. Proceedings of the International Congress of Mathematicians, 1, 1986.
- Representation theory, volume 129 of Graduate Texts in Mathematics. Springer-Verlag, New York, 1991. A first course, Readings in Mathematics.
- Polynomial Functors from Algebras over a Set-Operad and Nonlinear Mackey Functors. International Mathematics Research Notices, 2015(6):1461–1554, 2013.
- On the category of props. Appl. Categ. Structures, 23(4):543–573, 2015.
- Max Karoubi. Algèbres de Clifford et K-théorie. Ann. Sci. Ecole Norm. Sup., 1(4):161–270, 1968.
- On the wheeled PROP of stable cohomology of Aut(Fn)Autsubscript𝐹𝑛{\rm Aut}(F_{n})roman_Aut ( italic_F start_POSTSUBSCRIPT italic_n end_POSTSUBSCRIPT ) with bivariant coefficients. Algebr. Geom. Topol., 23(7):3089–3128, 2023.
- J.-L. Loday and B. Vallette. Algebraic operads, volume 346 of Grundlehren der Mathematischen Wissenschaften. Springer, 2012.
- Martin Markl. Operads and props, handbook of algebra. Elsevier/North-Holland, Amsterdam, 5:87–140, 2008.
- Barry Mitchell. The dominion of Isbell. Trans. Amer. Math. Soc., 167:319–331, 1972.
- S. Mac Lane. Categorical algebra. Bull. Amer. Math. Soc., 71:40–106, 1965.
- Christine Vespa. Extensions between functors from free groups. Bulletin of the London Mathematical Society, 50(3):401–419, 2018.
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