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In category theory, a finitely generated object is the quotient of a free object over a finite set, in the sense that it is the target of a regular epimorphism from a free object that is free on a finite set.
For instance, one way of defining a finitely generated group is that it is the image of a group homomorphism from a finitely generated free group.
See also
References
- finitely generated object at the nLab.
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