@MISC{YELLOW18.MIZ,
  AUTHOR = {Bancerek, Grzegorz},
  TITLE = {Concrete Categories},
  SECTION1 = {Definability of Categories and Functors},
  SECTION2 = {Isomorphism and Equivalence of Categories},
  SECTION3 = {Dual Categories},
  SECTION4 = {Concrete Categories},
  SECTION5 = {Equivalence Between Concrete Categories},
  SECTION6 = {Concretization of Categories},
  DAY = {12},
  MONTH = {January},
  YEAR = {2001},
  ADDRESS1 = {University of Bia{\l}ystok\\Shinshu University, Nagano},
  SUMMARY = {In the paper, we develop the notation of duality and equivalence of
 categories and concrete categories based on \cite{ALTCAT_1.ABS}.
 The development was motivated by the duality theory for continuous
 lattices (see \cite[p. 189]{CCL}), where we need to cope with
 concrete categories of lattices and maps preserving their properties.
 For example, the category {\it UPS} of complete lattices and directed
 suprema preserving maps; or
 the category {\it INF} of complete lattices and infima preserving maps.
 As the main result of this paper it is shown that
 every category is isomorphic to its concretization (the concrete category
 with the same objects).
 Some useful schemes to construct categories and functors are also
 presented.}}

