Finitely generated object

{{Short description|Concept in category theory}}

{{Merge from|Finitely generated|discuss=Talk:Finitely generated object#Proposed merge of Finitely generated into Finitely generated object|date=March 2025}}

{{One source|date=February 2024}}

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.{{nlab|id=finitely+generated+object|title=finitely generated object}}.

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.