Homological Algebra Of Semimodules And Semicont... -

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

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

A key feature is the adaptation of and Tor functors. Since you cannot always "subtract" to find boundaries, homological algebra here often uses: Unlike traditional modules over a ring, are defined

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

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