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

## Examples of Category Structures

Andrzej Trybulec
Warsaw University, Bialystok

### Summary.

We continue the formalization of the category theory.

#### MML Identifier: ALTCAT_2

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

#### Contents (PDF format)

1. Preliminaries
2. An auxiliary notion
3. A bit of lambda calculus
4. More on old categories
5. Transforming an old category into a new one
6. More on new categories
7. The empty category
8. Subcategories

#### Bibliography

[1] Czeslaw Bylinski. Basic functions and operations on functions. Journal of Formalized Mathematics, 1, 1989.
[2] Czeslaw Bylinski. Binary operations. Journal of Formalized Mathematics, 1, 1989.
[3] Czeslaw Bylinski. Functions and their basic properties. Journal of Formalized Mathematics, 1, 1989.
[4] Czeslaw Bylinski. Functions from a set to a set. Journal of Formalized Mathematics, 1, 1989.
[5] Czeslaw Bylinski. Introduction to categories and functors. Journal of Formalized Mathematics, 1, 1989.
[6] Czeslaw Bylinski. Some basic properties of sets. Journal of Formalized Mathematics, 1, 1989.
[7] Czeslaw Bylinski. A classical first order language. Journal of Formalized Mathematics, 2, 1990.
[8] 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.
[9] Czeslaw Bylinski. Cartesian categories. Journal of Formalized Mathematics, 4, 1992.
[10] Artur Kornilowicz. On the group of automorphisms of universal algebra and many sorted algebra. Journal of Formalized Mathematics, 6, 1994.
[11] Malgorzata Korolkiewicz. Homomorphisms of many sorted algebras. Journal of Formalized Mathematics, 6, 1994.
[12] Beata Madras. Product of family of universal algebras. Journal of Formalized Mathematics, 5, 1993.
[13] Michal Muzalewski and Wojciech Skaba. Three-argument operations and four-argument operations. Journal of Formalized Mathematics, 2, 1990.
[14] Andrzej Trybulec. Tarski Grothendieck set theory. Journal of Formalized Mathematics, Axiomatics, 1989.
[15] Andrzej Trybulec. Tuples, projections and Cartesian products. Journal of Formalized Mathematics, 1, 1989.
[16] Andrzej Trybulec. Many-sorted sets. Journal of Formalized Mathematics, 5, 1993.
[17] Andrzej Trybulec. Many sorted algebras. Journal of Formalized Mathematics, 6, 1994.
[18] Andrzej Trybulec. Categories without uniqueness of \rm cod and \rm dom. Journal of Formalized Mathematics, 7, 1995.
[19] Zinaida Trybulec. Properties of subsets. Journal of Formalized Mathematics, 1, 1989.
[20] Edmund Woronowicz. Relations and their basic properties. Journal of Formalized Mathematics, 1, 1989.