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.
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...
Frequently used to study the global sections of semimodule sheaves on tropical varieties. 3. Semicontinuity and Stability The rank or homological dimension of a semimodule