@MISC{YELLOW21.MIZ,
  AUTHOR = {Bancerek, Grzegorz},
  TITLE = {Categorial Background for Duality Theory},
  SECTION1 = {Lattice-wise Categories},
  SECTION2 = {Equivalence of Lattice-wise Categories},
  SECTION3 = {{\it UPS} Category},
  SECTION4 = {Lattice-wise Subcategories},
  DAY = {01},
  MONTH = {August},
  YEAR = {2001},
  ADDRESS1 = {University of Bia{\l}ystok\\Shinshu University, Nagano},
  SUMMARY = {In the paper, we develop the notation of lattice-wise
 categories as concrete categories (see \cite{YELLOW18.ABS}) of lattices.
 Namely, the categories based on \cite{ALTCAT_1.ABS} 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.}}

