Categorial Background for Duality Theory
Grzegorz Bancerek · 2007
Summary. In the paper, we develop the notation of lattice-wise categories as concrete categories (see [10]) of lattices. Namely, the categories based on [24] with lattices as objects and at least monotone maps between them as morphisms. As examples, we introduce the categories UPS, CONT, and ALG with complete, continuous, and algebraic lattices, respectively, as objects and directed suprema preserving maps as morphisms. Some useful schemes to construct categories of lattices and functors between them are also presented.