Essentially surjective functor

In mathematics, specifically in category theory, a functor

is essentially surjective (or dense) if each object of is isomorphic to an object of the form for some object of .

Any functor that is part of an equivalence of categories is essentially surjective. As a partial converse, any full and faithful functor that is essentially surjective is part of an equivalence of categories.[1]

Notes
  1. Mac Lane (1998), Theorem IV.4.1
gollark: Well, floating pointers™ would have greater dynamic range.
gollark: Hmm, wait, that's only for multiplication by two and bitshifts are cheap anyway.
gollark: Plus, multiplication is probably more efficient since you just change the exponent a bit.
gollark: Sad!
gollark: Oh, and compatibility with GPUs of course.

References
  • Mac Lane, Saunders (September 1998). Categories for the Working Mathematician (second ed.). Springer. ISBN 0-387-98403-8.
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