Adjoints, multi-adjoints, pluri-adjoints

Starting from a family of categoriesAp ,w herep ranges over a set P of indices, and functors Gp : Ap!X , p2 P ,w hereX is a category and each Gp has a left adjointFp, we construct a categoryA and a functorG : A!X that has a multi-adjoint in the sense of Y. Diers, and then a categoryA and a functor G :A!X that has a pluri-adjoint in the sense of the authors. These constructions show, at least in this instance, how the transition from adjoints to multi-adjoints to pluri-adjoints is performed. The problem of the existence and the characterization of a general class of pluri-adjoints arising in this manner invites further study.