We construct a combinatorial abstraction of the Leray spectral sequence and Morgan model associated with tropical compactifications of a complex hyperplane arrangement complement. We show that its homological properties generalise the ones that we expect from topology in the realizable case.

Geometric and Hodge-theoretic arguments are replaced by combinatorial blowups, Groebner bases, and sheaves on posets. This is joint work with Christin Bibby and Eva Maria Feichtner.