Journal of Formalized Mathematics
Volume 6, 1994
University of Bialystok
Copyright (c) 1994 Association of Mizar Users

## Categorial Categories and Slice Categories

Grzegorz Bancerek
Institute of Mathematics, Polish Academy of Sciences

### Summary.

By categorial categories we mean categories with categories as objects and morphisms of the form \$(C_1, C_2, F)\$, where \$C_1\$ and \$C_2\$ are categories and \$F\$ is a functor from \$C_1\$ into \$C_2\$.

#### MML Identifier: CAT_5

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

#### Contents (PDF format)

1. Categories with Triple-like Morphisms
2. Categorial Categories
3. Slice Categories
4. Functors Between Slice Categories

#### Bibliography

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[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. The modification of a function by a function and the iteration of the composition of a function. Journal of Formalized Mathematics, 2, 1990.
[8] Czeslaw Bylinski. Subcategories and products of categories. Journal of Formalized Mathematics, 2, 1990.
[9] Andrzej Trybulec. Domains and their Cartesian products. Journal of Formalized Mathematics, 1, 1989.
[10] Andrzej Trybulec. Tarski Grothendieck set theory. Journal of Formalized Mathematics, Axiomatics, 1989.
[11] Andrzej Trybulec. Tuples, projections and Cartesian products. Journal of Formalized Mathematics, 1, 1989.
[12] Andrzej Trybulec. Function domains and Fr\aenkel operator. Journal of Formalized Mathematics, 2, 1990.
[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.