Journal of Formalized Mathematics
Volume 8, 1996
University of Bialystok
Copyright (c) 1996 Association of Mizar Users

On the Category of Posets


Adam Grabowski
Warsaw University, Bialystok

Summary.

In the paper the construction of a category of partially ordered sets is shown: in the second section according to [6] and in the third section according to the definition given in [17]. Some of useful notions such as monotone map and the set of monotone maps between relational structures are given.

MML Identifier: ORDERS_3

The terminology and notation used in this paper have been introduced in the following articles [13] [8] [19] [20] [22] [4] [2] [14] [1] [7] [3] [11] [21] [12] [18] [6] [9] [15] [16] [5] [10] [17]

Contents (PDF format)

  1. Preliminaries
  2. On the Category of Posets
  3. On the Alternative Category of Posets

Bibliography

[1] Grzegorz Bancerek. The well ordering relations. Journal of Formalized Mathematics, 1, 1989.
[2] Grzegorz Bancerek. Categorial categories and slice categories. Journal of Formalized Mathematics, 6, 1994.
[3] Czeslaw Bylinski. Binary operations. Journal of Formalized Mathematics, 1, 1989.
[4] Czeslaw Bylinski. Functions and their basic properties. Journal of Formalized Mathematics, 1, 1989.
[5] Czeslaw Bylinski. Functions from a set to a set. Journal of Formalized Mathematics, 1, 1989.
[6] Czeslaw Bylinski. Introduction to categories and functors. Journal of Formalized Mathematics, 1, 1989.
[7] Czeslaw Bylinski. Partial functions. Journal of Formalized Mathematics, 1, 1989.
[8] Czeslaw Bylinski. Some basic properties of sets. Journal of Formalized Mathematics, 1, 1989.
[9] Czeslaw Bylinski. Category Ens. Journal of Formalized Mathematics, 3, 1991.
[10] Beata Madras. Product of family of universal algebras. Journal of Formalized Mathematics, 5, 1993.
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[14] Andrzej Trybulec. Tuples, projections and Cartesian products. Journal of Formalized Mathematics, 1, 1989.
[15] Andrzej Trybulec. Function domains and Fr\aenkel operator. Journal of Formalized Mathematics, 2, 1990.
[16] Andrzej Trybulec. Many-sorted sets. Journal of Formalized Mathematics, 5, 1993.
[17] Andrzej Trybulec. Categories without uniqueness of \rm cod and \rm dom. Journal of Formalized Mathematics, 7, 1995.
[18] Wojciech A. Trybulec. Partially ordered sets. Journal of Formalized Mathematics, 1, 1989.
[19] Zinaida Trybulec. Properties of subsets. Journal of Formalized Mathematics, 1, 1989.
[20] Edmund Woronowicz. Relations and their basic properties. Journal of Formalized Mathematics, 1, 1989.
[21] Edmund Woronowicz. Relations defined on sets. Journal of Formalized Mathematics, 1, 1989.
[22] Edmund Woronowicz and Anna Zalewska. Properties of binary relations. Journal of Formalized Mathematics, 1, 1989.

Received January 22, 1996

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