Categorial Background for Duality Theory

Grzegorz Bancerek

University of Bialystok, Shinshu University, Nagano

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 {\it UPS}, {\it CONT}, and {\it 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.

MML Identifier: YELLOW21

Contents (PDF format)

1. Lattice-wise Categories
2. Equivalence of Lattice-wise Categories
3. {\it UPS} Category
4. Lattice-wise Subcategories

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