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The category $\operatorname{STROP}$ of commutative semirings, whose morphismsare transmissions, is a full and reflective subcategory of the category$\operatorname{STROP}_m$ of supertropical monoids. Equivalence relations onsupertropical monoids are constructed easily, and utilized effectively forsupertropical semirings, whereas ideals are too special for semirings. Aimingfor tangible factorizations, certain types of such equivalence relations areconstructed and classified explicitly in this paper, followed by a profoundstudy of their characteristic properties with special emphasis on difficultiesarising from ghost products of tangible elements.

Supertropical Monoids II: Lifts, Transmissions, and Equalizers