Volume 13, 2001

University of Bialystok

Copyright (c) 2001 Association of Mizar Users

**Grzegorz Bancerek**- University of Bialystok, Shinshu University, Nagano

- In the paper we show useful facts concerning reverse and inclusion functors and the restriction of functors. We also introduce a new notation for the intersection of categories and the isomorphism under arbitrary functors.

- Reverse Functors
- Intersection of Categories
- Subcategories
- Inclusion Functors and Functor Restrictions
- Isomorphisms under Arbitrary Functor

- [1]
Grzegorz Bancerek.
Concrete categories.
*Journal of Formalized Mathematics*, 13, 2001. - [2]
Czeslaw Bylinski.
Basic functions and operations on functions.
*Journal of Formalized Mathematics*, 1, 1989. - [3]
Czeslaw Bylinski.
Binary operations.
*Journal of Formalized Mathematics*, 1, 1989. - [4]
Czeslaw Bylinski.
Functions and their basic properties.
*Journal of Formalized Mathematics*, 1, 1989. - [5]
Czeslaw Bylinski.
Functions from a set to a set.
*Journal of Formalized Mathematics*, 1, 1989. - [6]
Czeslaw Bylinski.
Partial functions.
*Journal of Formalized Mathematics*, 1, 1989. - [7]
Czeslaw Bylinski.
Some basic properties of sets.
*Journal of Formalized Mathematics*, 1, 1989. - [8]
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. - [9]
Artur Kornilowicz.
The composition of functors and transformations in alternative categories.
*Journal of Formalized Mathematics*, 10, 1998. - [10]
Malgorzata Korolkiewicz.
Homomorphisms of many sorted algebras.
*Journal of Formalized Mathematics*, 6, 1994. - [11]
Beata Madras.
Product of family of universal algebras.
*Journal of Formalized Mathematics*, 5, 1993. - [12]
Michal Muzalewski and Wojciech Skaba.
Three-argument operations and four-argument operations.
*Journal of Formalized Mathematics*, 2, 1990. - [13]
Andrzej Trybulec.
Tarski Grothendieck set theory.
*Journal of Formalized Mathematics*, Axiomatics, 1989. - [14]
Andrzej Trybulec.
Tuples, projections and Cartesian products.
*Journal of Formalized Mathematics*, 1, 1989. - [15]
Andrzej Trybulec.
Many-sorted sets.
*Journal of Formalized Mathematics*, 5, 1993. - [16]
Andrzej Trybulec.
Many sorted algebras.
*Journal of Formalized Mathematics*, 6, 1994. - [17]
Andrzej Trybulec.
Categories without uniqueness of \rm cod and \rm dom.
*Journal of Formalized Mathematics*, 7, 1995. - [18]
Andrzej Trybulec.
Examples of category structures.
*Journal of Formalized Mathematics*, 8, 1996. - [19]
Andrzej Trybulec.
Functors for alternative categories.
*Journal of Formalized Mathematics*, 8, 1996. - [20]
Zinaida Trybulec.
Properties of subsets.
*Journal of Formalized Mathematics*, 1, 1989. - [21]
Edmund Woronowicz.
Relations and their basic properties.
*Journal of Formalized Mathematics*, 1, 1989. - [22]
Edmund Woronowicz.
Relations defined on sets.
*Journal of Formalized Mathematics*, 1, 1989.

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