Incidence Categories
Szczesny, Matt
Original · EN
Given a family of posets closed under disjoint unions and the operation of taking convex subposets, we construct a category called the incidence category of. This category is "nearly abelian" in the sense that all morphisms have kernels/cokernels, and possesses a symmetric monoidal structure akin to direct sum. The Ringel-Hall algebra of is isomorphic to the incidence Hopf algebra of the collection ¶() of order ideals of posets in. This construction generalizes the categories introduced by K. Kremnizer and the author In the case when is the collection of posets coming from rooted forests or Feynman graphs.
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