Generator (category theory)
- Generator (category theory)
In category theory in mathematics a generator (or separator) of a category is an object "G" of the category, such that for any two different morphisms in , there is a morphism , such that the compositions .
Examples
* In the category of abelian groups, the group of integers is a generator: If "f" and "g" are different, then there is an element , such that . Hence the map , suffices.
* Similarly, the one-point set is a generator for the category of sets.
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