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Directed hereditary species and decomposition spaces

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arxiv 2211.07721 v2 pith:EDAPHS36 submitted 2022-11-14 math.CO math.ATmath.CT

Alex Cebrian , Wilson Forero This is my paper · ORCID
classification math.COmath.ATmath.CT
keywords comoduledirectedspacesspeciesbialgebradecompositionhereditaryalvez--kock--tonks
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We introduce the notion of directed hereditary species and show that they have associated monoidal decomposition spaces, comodule bialgebras, and operadic categories. The notion subsumes Schmitt's hereditary species, G\'alvez--Kock--Tonks directed restrictions species, and a directed version of Carlier's construction of monoidal decomposition spaces and comodule bialgebras. In addition to all the examples of Schmitt, G\'alvez--Kock--Tonks and Carlier, the new construction covers also the Fauvet--Foissy--Manchon comodule bialgebra of finite topological spaces, the Calaque--Ebrahimi-Fard--Manchon comodule bialgebra of rooted trees, and the Fa\`a di Bruno comodule bialgebra of linear trees.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Preorders on maximal chains: hyperplane arrangements, Cambrian lattices, and maximal green sequences

    math.CO 2025-06 conditional novelty 8.0 of 10

    Edge-labelled polygonal lattices carry preorders on square-equivalence classes of maximal chains that descend to contractions under lattice quotients, yielding new structural results for Cambrian lattices and the Kapr...

  2. Pita factorisation in operadic categories

    math.CT 2025-12 conditional novelty 6.0 of 10

    For strictly factorisable operadic categories, the pita nerve is a coherent top-lax simplicial category, and a decomposition space when all quasibijections are invertible.

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