The story
Etymology from Wiktionary, CC BY-SA 4.0.
Today it means: 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). Full definition →
Etymology from Wiktionary, CC BY-SA 4.0.