Volume 2, 1990

University of Bialystok

Copyright (c) 1990 Association of Mizar Users

**Czeslaw Bylinski**- Warsaw University, Bialystok
- Supported by RPBP.III-24.C1.

- The {\it subcategory} of a category and product of categories is defined. The {\it inclusion functor} is the injection (inclusion) map $E \atop \hookrightarrow$ which sends each object and each arrow of a Subcategory $E$ of a category $C$ to itself (in $C$). The inclusion functor is faithful. {\it Full subcategories} of $C$, that is, those subcategories $E$ of $C$ such that $\hbox{Hom}_E(a,b) = \hbox{Hom}_C(b,b)$ for any objects $a,b$ of $E$, are defined. A subcategory $E$ of $C$ is full when the inclusion functor $E \atop \hookrightarrow$ is full. The proposition that a full subcategory is determined by giving the set of objects of a category is proved. The product of two categories $B$ and $C$ is constructed in the usual way. Moreover, some simple facts on $bifunctors$ (functors from a product category) are proved. The final notions in this article are that of projection functors and product of two functors ({\it complex} functors and {\it product} functors).

Contents (PDF format)

- [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.
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]
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.
Function domains and Fr\aenkel operator.
*Journal of Formalized Mathematics*, 2, 1990. - [12]
Zinaida Trybulec.
Properties of subsets.
*Journal of Formalized Mathematics*, 1, 1989. - [13]
Edmund Woronowicz.
Relations and their basic properties.
*Journal of Formalized Mathematics*, 1, 1989.

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