Volume 4, 1992

University of Bialystok

Copyright (c) 1992 Association of Mizar Users

**Andrzej Trybulec**- Warsaw University, Bialystok

- We define some well known isomorphisms between functor categories: between $A^{\mathop{\dot\circlearrowright}(o,m)}$ and $A$, between $C^{\mizleftcart A,B\mizrightcart}$ and ${(C^B)}^A$, and between ${\mizleftcart B,C\mizrightcart}^A$ and $\mizleftcart B^A,C^A\mizrightcart$. Compare [9] and [8]. Unfortunately in this paper "functor" is used in two different meanings, as a lingual function and as a functor between categories.

- Preliminaries
- The isomorphism between $A^{\mathop{\dot\circlearrowright}(o,m)}$ and $A$
- The isomorphism between $C^{\mizleftcart A,B\mizrightcart}$ and ${(C^B)}^A$
- The isomorphism between ${\mizleftcart B,C\mizrightcart}^A$ and $\mizleftcart B^A,C^A\mizrightcart$

- [1]
Grzegorz Bancerek.
Curried and uncurried functions.
*Journal of Formalized Mathematics*, 2, 1990. - [2]
Czeslaw Bylinski.
Basic functions and operations on functions.
*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.
Subcategories and products of categories.
*Journal of Formalized Mathematics*, 2, 1990. - [8] Saunders Mac Lane. \em Categories for the Working Mathematician, volume 5 of \em Graduate Texts in Mathematics. Springer Verlag, New York, Heidelberg, Berlin, 1971.
- [9] Zbigniew Semadeni and Antoni Wiweger. \em Wst\c ep do teorii kategorii i funktorow, volume 45 of \em Biblioteka Matematyczna. PWN, Warszawa, 1978.
- [10]
Andrzej Trybulec.
Tarski Grothendieck set theory.
*Journal of Formalized Mathematics*, Axiomatics, 1989. - [11]
Andrzej Trybulec.
Function domains and Fr\aenkel operator.
*Journal of Formalized Mathematics*, 2, 1990. - [12]
Andrzej Trybulec.
Isomorphisms of categories.
*Journal of Formalized Mathematics*, 3, 1991. - [13]
Andrzej Trybulec.
Natural transformations. Discrete categories.
*Journal of Formalized Mathematics*, 3, 1991. - [14]
Zinaida Trybulec.
Properties of subsets.
*Journal of Formalized Mathematics*, 1, 1989. - [15]
Edmund Woronowicz.
Relations and their basic properties.
*Journal of Formalized Mathematics*, 1, 1989. - [16]
Edmund Woronowicz.
Relations defined on sets.
*Journal of Formalized Mathematics*, 1, 1989.

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