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
Constructing resolutions using free semimodules or injective envelopes (like the "max-plus" analogues of vector spaces). Homological Algebra of Semimodules and Semicont...
The "Semicontinuity" aspect typically refers to the behavior of dimensions (like the rank of a semimodule) under deformations. algebra)
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 algebra). Because semimodules lack additive inverses
The rank or homological dimension of a semimodule often drops at specific points of a parameter space, mirroring the behavior of coherent sheaves in algebraic geometry.