Homological Algebra Of Semimodules And Semicont... (2025)

Unlike traditional modules over a ring, are defined over semirings (like the

A key feature is the adaptation of and Tor functors. Since you cannot always "subtract" to find boundaries, homological algebra here often uses: Homological Algebra of Semimodules and Semicont...

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. Unlike traditional modules over a ring, are defined

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. Unlike traditional modules over a ring