Results on the use of category theory for the study of lattice-valued finite state machines

In this paper, we introduce the concepts of category of lattice-valued finite state machines, category of quasi-lattice-valued transformation semigroups, category of quasi-lattice-valued transformation monoids, category of lattice-valued transformation semigroups, category of lattice-valued transformation monoids and six pairs of functors, each pair of functors have the adjoint property, we discuss the relation between the categories with functors and give the adjoint theorems and relation theorems.