Supertropical Monoids III: Factorization and splitting covers

The category [Formula: see text] of supertropical monoids, whose morphisms are transmissions, has the full-reflective subcategory [Formula: see text] of commutative semirings. In this setup, quotients are determined directly by equivalence relations, as ideals are not applicable for monoids, leading to a new approach to factorization theory. To this end, tangible factorization into irreducibles is obtained through fiber contractions and their hierarchy. Fiber contractions also provide different quotient structures, associated with covers and types of splitting covers.