Journal of Formalized Mathematics
Volume 3, 1991
University of Bialystok
Copyright (c) 1991
Association of Mizar Users
Categories of Groups

Michal Muzalewski

Warsaw University, Bialystok
Summary.

We define the category of groups and its subcategories: category
of Abelian groups and category of groups with the operator of $1/2$.
The carriers of the groups are included in a universum. The universum
is a parameter of the categories.
MML Identifier:
GRCAT_1
The terminology and notation used in this paper have been
introduced in the following articles
[14]
[6]
[17]
[18]
[2]
[15]
[1]
[16]
[8]
[10]
[5]
[4]
[13]
[3]
[7]
[12]
[9]
[11]
Contents (PDF format)
Bibliography
 [1]
Czeslaw Bylinski.
Binary operations.
Journal of Formalized Mathematics,
1, 1989.
 [2]
Czeslaw Bylinski.
Functions and their basic properties.
Journal of Formalized Mathematics,
1, 1989.
 [3]
Czeslaw Bylinski.
Functions from a set to a set.
Journal of Formalized Mathematics,
1, 1989.
 [4]
Czeslaw Bylinski.
Introduction to categories and functors.
Journal of Formalized Mathematics,
1, 1989.
 [5]
Czeslaw Bylinski.
Partial functions.
Journal of Formalized Mathematics,
1, 1989.
 [6]
Czeslaw Bylinski.
Some basic properties of sets.
Journal of Formalized Mathematics,
1, 1989.
 [7]
Czeslaw Bylinski.
Subcategories and products of categories.
Journal of Formalized Mathematics,
2, 1990.
 [8]
Eugeniusz Kusak, Wojciech Leonczuk, and Michal Muzalewski.
Abelian groups, fields and vector spaces.
Journal of Formalized Mathematics,
1, 1989.
 [9]
Michal Muzalewski.
Midpoint algebras.
Journal of Formalized Mathematics,
1, 1989.
 [10]
Michal Muzalewski.
Construction of rings and left, right, and bimodules over a ring.
Journal of Formalized Mathematics,
2, 1990.
 [11]
Michal Muzalewski.
Atlas of midpoint algebra.
Journal of Formalized Mathematics,
3, 1991.
 [12]
Michal Muzalewski and Wojciech Skaba.
From loops to abelian multiplicative groups with zero.
Journal of Formalized Mathematics,
2, 1990.
 [13]
Bogdan Nowak and Grzegorz Bancerek.
Universal classes.
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]
Wojciech A. Trybulec.
Vectors in real linear space.
Journal of Formalized Mathematics,
1, 1989.
 [17]
Zinaida Trybulec.
Properties of subsets.
Journal of Formalized Mathematics,
1, 1989.
 [18]
Edmund Woronowicz.
Relations and their basic properties.
Journal of Formalized Mathematics,
1, 1989.
Received October 3, 1991
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