The polyhedral geometry of Wajsberg hoops

Abstract We show that the algebraic category of finitely presented Wajsberg hoops is equivalent to a non-full subcategory MV-algebras. use this connection how methods and techniques developed study MV-algebras can be adapted hoops, as well. In particular, we are dually rational polyhedra with $\mathbb {Z}$-maps. duality provide geometrical characterization generated projective exact hoops. As applications, logical properties $0$-free fragment Łukasiewicz logic, seen substructural logic. that, while deducibility in among 0-free formulas same not true for admissibility rules: there rules written language admissible but Moreover, unification type nullary, unitary, therefore showing decidability fragment.