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.
algebra). Because semimodules lack additive inverses, they do not form an abelian category. This necessitates a shift from exact sequences to and kernel-like structures based on congruences. 2. Derived Functors in Non-Additive Settings Homological Algebra of Semimodules and Semicont...
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