Posets with interfaces as a model for concurrency

We introduce posets with interfaces (iposets) and generalise their standard serial composition to a new gluing composition. In the partial order semantics of concurrency, allow modelling events that extend in time across components. Alternatively, taking decompositional view, cutting through events, while may only cut edges poset. show iposets under form category, which generalises monoid up isomorphism. They 2-category when subsumption lax tensor non-commutative parallel are added, interchange monoids used for series-parallel posets. also study gluing-parallel hierarchy iposets, one. The class contains interval orders, well studied concurrency theory, too. it is strictly contained all by identifying several forbidden substructures.