Journal of Formalized Mathematics
Volume 3, 1991
University of Bialystok
Copyright (c) 1991 Association of Mizar Users

## Category Ens

Czeslaw Bylinski
Warsaw University, Bialystok

### Summary.

If $V$ is any non-empty set of sets, we define $\hbox{\bf Ens}_V$ to be the category with the objects of all sets $X \in V$, morphisms of all mappings from $X$ into $Y$, with the usual composition of mappings. By a mapping we mean a triple $\langle X,Y,f \rangle$ where $f$ is a function from $X$ into $Y$. The notations and concepts included corresponds to that presented in [12], [10]. We also introduce representable functors to illustrate properties of the category {\bf Ens}.

#### MML Identifier: ENS_1

The terminology and notation used in this paper have been introduced in the following articles [15] [6] [18] [16] [14] [19] [2] [3] [5] [7] [1] [17] [11] [13] [4] [8] [9]

#### Contents (PDF format)

1. Mappings
2. Category Ens
3. Representable Functors

#### Acknowledgments

I would like to thank Andrzej Trybulec for his useful suggestions and valuable comments.

#### Bibliography

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