Categories of Algebraic Contexts Equivalent to Idempotent Semirings and Domain Semirings

Abstract

A categorical equivalence between algebraic contexts with relational morphisms and join-semilattices with homomorphisms is presented and extended to idempotent semirings and domain semirings. These contexts are the Kripke structures for idempotent semirings and allow more efficient computations on finite models because they can be logarithmically smaller than the original semiring. Some examples and constructions such as matrix semirings are also considered.