The category of hyper residuated lattices

In this paper, first we consider homomorphisms and also strong homomorphisms between hyper residuated lattices, and their properties are presented. Then we use strong homomorphisms to introduce the category of hyper residuated lattices. We show that this category is neither complete but not cocomplete. Moreover, we find some conditions under which the equalizers and pullbacks exist. Finally, we verify subdirectly irreducible hyper residuated lattices and attempt to construct a hyper residuated lattice from a residuated lattice.