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

Examples of Category Structures


Adam Grabowski
Warsaw University, Bialystok

Summary.

This article contains definitions of two category structures: the category of many sorted signatures and the category of many sorted algebras. Some facts about these structures are proved.

MML Identifier: MSINST_1

The terminology and notation used in this paper have been introduced in the following articles [16] [8] [21] [20] [22] [5] [6] [23] [7] [9] [1] [4] [15] [2] [17] [13] [18] [12] [19] [14] [11] [3] [10]

Contents (PDF format)

  1. Category of Many Sorted Signatures
  2. Category of Many Sorted Algebras

Bibliography

[1] Grzegorz Bancerek. K\"onig's theorem. Journal of Formalized Mathematics, 2, 1990.
[2] Grzegorz Bancerek. Cartesian product of functions. Journal of Formalized Mathematics, 3, 1991.
[3] Grzegorz Bancerek. Translations, endomorphisms, and stable equational theories. Journal of Formalized Mathematics, 8, 1996.
[4] Czeslaw Bylinski. Binary operations. Journal of Formalized Mathematics, 1, 1989.
[5] Czeslaw Bylinski. Functions and their basic properties. Journal of Formalized Mathematics, 1, 1989.
[6] Czeslaw Bylinski. Functions from a set to a set. 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. Finite sequences and tuples of elements of a non-empty sets. Journal of Formalized Mathematics, 2, 1990.
[10] Adam Grabowski. Inverse limits of many sorted algebras. Journal of Formalized Mathematics, 8, 1996.
[11] Artur Kornilowicz. On the group of automorphisms of universal algebra and many sorted algebra. Journal of Formalized Mathematics, 6, 1994.
[12] Malgorzata Korolkiewicz. Homomorphisms of many sorted algebras. Journal of Formalized Mathematics, 6, 1994.
[13] Beata Madras. Product of family of universal algebras. Journal of Formalized Mathematics, 5, 1993.
[14] Beata Madras. Products of many sorted algebras. Journal of Formalized Mathematics, 6, 1994.
[15] Michal Muzalewski and Wojciech Skaba. Three-argument operations and four-argument operations. Journal of Formalized Mathematics, 2, 1990.
[16] Andrzej Trybulec. Tarski Grothendieck set theory. Journal of Formalized Mathematics, Axiomatics, 1989.
[17] Andrzej Trybulec. Many-sorted sets. Journal of Formalized Mathematics, 5, 1993.
[18] Andrzej Trybulec. Many sorted algebras. Journal of Formalized Mathematics, 6, 1994.
[19] Andrzej Trybulec. Categories without uniqueness of \rm cod and \rm dom. Journal of Formalized Mathematics, 7, 1995.
[20] Andrzej Trybulec. Subsets of real numbers. Journal of Formalized Mathematics, Addenda, 2003.
[21] Zinaida Trybulec. Properties of subsets. Journal of Formalized Mathematics, 1, 1989.
[22] Edmund Woronowicz. Relations and their basic properties. Journal of Formalized Mathematics, 1, 1989.
[23] Edmund Woronowicz. Relations defined on sets. Journal of Formalized Mathematics, 1, 1989.

Received June 11, 1996


[ Download a postscript version, MML identifier index, Mizar home page]