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.

Received January 22, 1996


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