subfunctor

English

Etymology

sub- +‎ functor

Noun

subfunctor (plural subfunctors)

1. (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).
   • 2015, Serge Bouc, Jacques Thévenaz, “The representation theory of finite sets and correspondences”, in arXiv‎^[1]:

     Also, if $k$ is noetherian, then any subfunctor of a finitely generated functor is finitely generated.