Categorical notions of layered tropical algebra and geometry

Abstract

This paper supplements [17], showing that categorically the layered theory is the same as the theory of ordered monoids (e.g. the max-plus algebra) used in tropical mathematics. A layered theory is developed in the context of categories, together with a "tropicalization functor" which permits us to pass from usual algebraic geometry to the tropical world. We consider tropical varieties from this categorical viewpoint, with emphasis on polynomial functions and their roots.

34 pages

References in corpus (3)

• Patchworking singular algebraic curves, non-Archimedean amoebas and enumerative geometry
• Categories of layered semirings
• Supertropical Monoids: Basics, Canonical Factorization, and Lifting Ghosts to Tangibles

Cited by in corpus (1)

• Categories of layered semirings