Journal of Formalized Mathematics
Volume 4, 1992
University of Bialystok
Copyright (c) 1992 Association of Mizar Users

## Products and Coproducts in Categories

Czeslaw Bylinski
Warsaw University, Bialystok

### Summary.

A product and coproduct in categories are introduced. The concepts included correspond to that presented in [6].

#### MML Identifier: CAT_3

The terminology and notation used in this paper have been introduced in the following articles [8] [10] [11] [1] [7] [4] [2] [9] [3] [5]

#### Contents (PDF format)

1. Indexed families
2. Indexed families of morphisms
3. Retractions and coretractions
4. Morphisms determined by a terminal object
5. Morphisms determined by an initial object
6. Products
7. Coproducts

#### Bibliography

[1] Czeslaw Bylinski. Functions and their basic properties. Journal of Formalized Mathematics, 1, 1989.
[2] Czeslaw Bylinski. Functions from a set to a set. Journal of Formalized Mathematics, 1, 1989.
[3] Czeslaw Bylinski. Introduction to categories and functors. Journal of Formalized Mathematics, 1, 1989.
[4] Czeslaw Bylinski. The modification of a function by a function and the iteration of the composition of a function. Journal of Formalized Mathematics, 2, 1990.
[5] Czeslaw Bylinski. Opposite categories and contravariant functors. Journal of Formalized Mathematics, 3, 1991.
[6] Zbigniew Semadeni and Antoni Wiweger. \em Wst\c ep do teorii kategorii i funktorow, volume 45 of \em Biblioteka Matematyczna. PWN, Warszawa, 1978.
[7] Andrzej Trybulec. Binary operations applied to functions. Journal of Formalized Mathematics, 1, 1989.
[8] Andrzej Trybulec. Tarski Grothendieck set theory. Journal of Formalized Mathematics, Axiomatics, 1989.
[9] Wojciech A. Trybulec. Pigeon hole principle. Journal of Formalized Mathematics, 2, 1990.
[10] Zinaida Trybulec. Properties of subsets. Journal of Formalized Mathematics, 1, 1989.
[11] Edmund Woronowicz. Relations and their basic properties. Journal of Formalized Mathematics, 1, 1989.