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

## Products of Many Sorted Algebras

Warsaw University, Bialystok

### Summary.

Product of two many sorted universal algebras and product of family of many sorted universal algebras are defined in this article. Operations on functions, such that commute, Frege, are also introduced.

#### MML Identifier: PRALG_2

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

#### Contents (PDF format)

1. Preliminaries
2. Operations on Functions
3. Family of Many Sorted Universal Algebras
4. Product of Many Sorted Universal Algebras

#### Bibliography

[1] Grzegorz Bancerek. Curried and uncurried functions. Journal of Formalized Mathematics, 2, 1990.
[2] Grzegorz Bancerek. K\"onig's theorem. Journal of Formalized Mathematics, 2, 1990.
[3] Grzegorz Bancerek. Cartesian product of functions. Journal of Formalized Mathematics, 3, 1991.
[4] Grzegorz Bancerek and Piotr Rudnicki. On defining functions on trees. Journal of Formalized Mathematics, 5, 1993.
[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. Some basic properties of sets. Journal of Formalized Mathematics, 1, 1989.
[8] Czeslaw Bylinski. A classical first order language. Journal of Formalized Mathematics, 2, 1990.
[9] Czeslaw Bylinski. Finite sequences and tuples of elements of a non-empty sets. Journal of Formalized Mathematics, 2, 1990.
[10] Beata Madras. Product of family of universal algebras. Journal of Formalized Mathematics, 5, 1993.
[11] Andrzej Trybulec. Tarski Grothendieck set theory. Journal of Formalized Mathematics, Axiomatics, 1989.
[12] Andrzej Trybulec. Tuples, projections and Cartesian products. Journal of Formalized Mathematics, 1, 1989.
[13] Andrzej Trybulec. Function domains and Fr\aenkel operator. Journal of Formalized Mathematics, 2, 1990.
[14] Andrzej Trybulec. Many-sorted sets. Journal of Formalized Mathematics, 5, 1993.
[15] Andrzej Trybulec. Many sorted algebras. Journal of Formalized Mathematics, 6, 1994.
[16] Zinaida Trybulec. Properties of subsets. Journal of Formalized Mathematics, 1, 1989.
[17] Edmund Woronowicz. Relations and their basic properties. Journal of Formalized Mathematics, 1, 1989.

Received April 25, 1994