Homological Algebra Of Semimodules And Semicont... -

Constructing resolutions using free semimodules or injective envelopes (like the "max-plus" analogues of vector spaces).

Frequently used to study the global sections of semimodule sheaves on tropical varieties. 3. Semicontinuity and Stability 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 Semicontinuity and Stability algebra)

The "Semicontinuity" aspect typically refers to the behavior of dimensions (like the rank of a semimodule) under deformations. Homological Algebra of Semimodules and Semicont...

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

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.