Given a family $\F$ of posets closed under disjoint unions and the operation of taking convex subposets, we construct a category $\C_{ \F}$ called the \emph{ incidence category of $\F$}. 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 $\C_{ \F}$ is isomorphic to the incidence Hopf algebra of the collection $\P(\F)$ of order ideals of posets in $\F$. This construction generalizes the categories introduced by K. Kremnizer and the author In the case when $\F$ is the collection of posets coming from rooted forests or Feynman graphs.
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