Hoop twist-structures

In this paper, we introduce hoop twist-structure whose members are built as special squares of an arbitrary hoop. We show how our construction relates to eN4-lattices (N4-lattices) and implicative twist-structures. We prove that hoop twist-structures form a quasi-variety and characterize the AHT-congruences of each algebra in this quasi-variety in terms of the congruences of the associated hoop.