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Pronunciation varies by accent · noun
(category theory) A functor such that all of the objects it maps are mapped by the parent functor, and for any arrow it maps the parent functor includes the same mapping (although it may also map arrows from the same domain to additional images outside the image of the subfunctor)..
Also, if k is noetherian, then any subfunctor of a finitely generated functor is finitely generated.
Use subfunctor when its meaning, tone and grammar fit the full sentence. A synonym is not always a direct replacement.
Subfunctor means (category theory) A functor such that all of the objects it maps are mapped by the parent functor, and for any arrow it maps the parent functor includes the same mapping (although it may also map arrows from the same domain to additional images outside the image of the subfunctor)..
The closest synonym depends on the sentence and intended sense.
The opposite depends on the specific sense.
Also, if k is noetherian, then any subfunctor of a finitely generated functor is finitely generated.
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