Essentially surjective functor explained

F:C\toD

is essentially surjective if each object

d

of

D

is isomorphic to an object of the form

Fc

for some object

c

of

C

.

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

References

. Saunders Mac Lane. Categories for the Working Mathematician. second. September 1998. Springer. 0-387-98403-8.

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