Homological Algebra Of Semimodules And Semicont... May 2026

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.

It connects to the Lusternik-Schnirelmann category in idempotent analysis, where semicontinuity helps track the stability of eigenvalues in max-plus linear systems. 4. Applications: Tropical Geometry Homological Algebra of Semimodules and Semicont...

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 This framework provides the "linear algebra" for tropical