Journal of Formalized Mathematics
Volume 4, 1992
University of Bialystok
Copyright (c) 1992 Association of Mizar Users

## Some Isomorphisms Between Functor Categories

Andrzej Trybulec
Warsaw University, Bialystok

### Summary.

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.

#### MML Identifier: ISOCAT_2

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

#### Contents (PDF format)

1. Preliminaries
2. The isomorphism between $A^{\mathop{\dot\circlearrowright}(o,m)}$ and $A$
3. The isomorphism between $C^{\mizleftcart A,B\mizrightcart}$ and ${(C^B)}^A$
4. The isomorphism between ${\mizleftcart B,C\mizrightcart}^A$ and $\mizleftcart B^A,C^A\mizrightcart$

#### Bibliography

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Received June 5, 1992