The "Semicontinuity" aspect typically refers to the behavior of dimensions (like the rank of a semimodule) under deformations.
This framework provides the "linear algebra" for tropical varieties. Just as homological algebra helps classify manifolds, semimodule homology helps classify and understand the intersections of tropical hypersurfaces. Homological Algebra of Semimodules and Semicont...
Unlike traditional modules over a ring, are defined over semirings (like the The "Semicontinuity" aspect typically refers to the behavior