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.

MML Identifier: MSUALG_1

Contents (PDF format)

1. Preliminaries
2. Auxiliary functors
3. Many sorted signatures
4. Many sorted algebras
5. Universal algebras as many sorted
6. Universal algebras for many sorted algebras with one sort

Acknowledgments

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 non-empty 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. Many-sorted 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.