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

[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.

Received June 5, 1992


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