Journal of Formalized Mathematics
Volume 13, 2001
University of Bialystok
Copyright (c) 2001 Association of Mizar Users

Concrete Categories


Grzegorz Bancerek
University of Bialystok, Shinshu University, Nagano

Summary.

In the paper, we develop the notation of duality and equivalence of categories and concrete categories based on [22]. The development was motivated by the duality theory for continuous lattices (see [10, p. 189]), 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.

MML Identifier: YELLOW18

The terminology and notation used in this paper have been introduced in the following articles [18] [9] [26] [25] [27] [28] [6] [8] [7] [16] [19] [5] [15] [2] [1] [20] [13] [21] [12] [4] [3] [22] [23] [24] [14] [17] [11]

Contents (PDF format)

  1. Definability of Categories and Functors
  2. Isomorphism and Equivalence of Categories
  3. Dual Categories
  4. Concrete Categories
  5. Equivalence Between Concrete Categories
  6. Concretization of Categories

Bibliography

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Received January 12, 2001


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