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]
-
Mappings
-
Category Ens
-
Representable Functors
Acknowledgments
I would like to thank Andrzej Trybulec for his useful suggestions and valuable
comments.
Bibliography
- [1]
Grzegorz Bancerek.
Curried and uncurried functions.
Journal of Formalized Mathematics,
2, 1990.
- [2]
Czeslaw Bylinski.
Functions and their basic properties.
Journal of Formalized Mathematics,
1, 1989.
- [3]
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Functions from a set to a set.
Journal of Formalized Mathematics,
1, 1989.
- [4]
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Introduction to categories and functors.
Journal of Formalized Mathematics,
1, 1989.
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Partial functions.
Journal of Formalized Mathematics,
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Some basic properties of sets.
Journal of Formalized Mathematics,
1, 1989.
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Journal of Formalized Mathematics,
3, 1991.
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- [13]
Andrzej Trybulec.
Binary operations applied to functions.
Journal of Formalized Mathematics,
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Andrzej Trybulec.
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Journal of Formalized Mathematics,
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Journal of Formalized Mathematics,
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1, 1989.
Received August 1, 1991
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