# Incidence Categories - Mathematics > Quantum Algebra

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Abstract: Given a family $\F$ of posets closed under disjoint unions and the operationof taking convex subposets, we construct a category $\C {\F}$ called the\emph{incidence category of $\F$}. This category is -nearly abelian- in thesense that all morphisms have kernels-cokernels, and possesses a symmetricmonoidal structure akin to direct sum. The Ringel-Hall algebra of $\C {\F}$ isisomorphic to the incidence Hopf algebra of the collection $\P\F$ of orderideals of posets in $\F$. This construction generalizes the categoriesintroduced by K. Kremnizer and the author In the case when $\F$ is thecollection of posets coming from rooted forests or Feynman graphs.

Autor: Matt Szczesny

Fuente: https://arxiv.org/