Journal of Formalized Mathematics
Volume 6, 1994
University of Bialystok
Copyright (c) 1994
Association of Mizar Users
Many Sorted Algebras

Andrzej Trybulec

Warsaw University, Bialystok
Summary.

The basic purpose of the paper is to prepare preliminaries of the
theory of many sorted algebras. The concept of the signature of a many
sorted algebra is introduced as well as the concept of many sorted algebra
itself. Some auxiliary related notions are defined.
The correspondence between (1 sorted) universal algebras [8]
and many sorted algebras with one sort only is described by
introducing two functors mapping one into the other. The construction
is done this way that the composition of both functors is the identity
on universal algebras.
The terminology and notation used in this paper have been
introduced in the following articles
[10]
[13]
[12]
[14]
[4]
[5]
[2]
[9]
[6]
[7]
[1]
[11]
[3]
[8]

Preliminaries

Auxiliary functors

Many sorted signatures

Many sorted algebras

Universal algebras as many sorted

Universal algebras for many sorted algebras with one sort
Acknowledgments
I would like to express my gratitude to Czes{\l}aw Byli\'nski,
whose remarks enabled me to enhance the paper.
Bibliography
 [1]
Grzegorz Bancerek.
K\"onig's theorem.
Journal of Formalized Mathematics,
2, 1990.
 [2]
Grzegorz Bancerek and Krzysztof Hryniewiecki.
Segments of natural numbers and finite sequences.
Journal of Formalized Mathematics,
1, 1989.
 [3]
Jozef Bialas.
Group and field definitions.
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.
Partial functions.
Journal of Formalized Mathematics,
1, 1989.
 [7]
Czeslaw Bylinski.
Finite sequences and tuples of elements of a nonempty sets.
Journal of Formalized Mathematics,
2, 1990.
 [8]
Jaroslaw Kotowicz, Beata Madras, and Malgorzata Korolkiewicz.
Basic notation of universal algebra.
Journal of Formalized Mathematics,
4, 1992.
 [9]
Andrzej Trybulec.
Binary operations applied to functions.
Journal of Formalized Mathematics,
1, 1989.
 [10]
Andrzej Trybulec.
Tarski Grothendieck set theory.
Journal of Formalized Mathematics,
Axiomatics, 1989.
 [11]
Andrzej Trybulec.
Manysorted sets.
Journal of Formalized Mathematics,
5, 1993.
 [12]
Andrzej Trybulec.
Subsets of real numbers.
Journal of Formalized Mathematics,
Addenda, 2003.
 [13]
Zinaida Trybulec.
Properties of subsets.
Journal of Formalized Mathematics,
1, 1989.
 [14]
Edmund Woronowicz.
Relations and their basic properties.
Journal of Formalized Mathematics,
1, 1989.
Received April 21, 1994
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