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== Introductory example ==
As an example, the set Ω = {0,1} is a subobject classifier in the category of sets and functions: to every subset ''U'' of ''X'' we can assign the function ''g'' from ''X'' to Ω that maps precisely the elements of ''U'' to 1 (see [[indicator function|characteristic function]]). Every function from ''X'' to Ω arises in this fashion from precisely one subset ''U''.
== Definition ==
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