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Line 3: == Introductory example == As an example, the set Ω = {0,1} is a subobject classifier in the [[category of sets]] and functions: to every subset   '' j '' : '' U A'' → '' X '' we can assign the function ''χ<sub>j</sub>'' from '' X '' to Ω that maps precisely the elements of ''UA'' to 1 (see [[indicator function\|characteristic function]]). Every function from ''X'' to Ω arises in this fashion from precisely one subset ''UA''. To be clearer, consider a [[subset]] ''A'' of ''S'' (''A'' ⊆ ''S''), where ''S'' is a set. The notion of being a subset can be expressed mathematically using the so-called characteristic function χ<sub>''A''</sub> : S → {0,1}, which is defined as follows:

Subobject classifier: Difference between revisions