description of logic. Note however that subobject classifiers are often much more complicated than the simple binary logic truth values {true, false}.

Introductory example

As an example, the set ? = {0,1} is a subobject classifier in the category of sets and functions: to every subset A of S defined by the inclusion function j : A -> S we can assign the function ?_A from S to ? that maps precisely the elements of A to 1, and the elements outside A to 0 (in other words,

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