Essentially Surjective Functor

Definition

Given a functor $F:\mathcal{C}\to \mathcal{D}$. $F$ is essentially surjective iff $\forall d:\mathcal{D}.\exists c:\mathcal{C}.F(c)\cong d$

Remarks

All surjective functors are essentially surjective. We need not have full surjectivity, but the image of the functor must contain at least one of every kind of object up to isomorphism.

Resources

https://math.stackexchange.com/questions/4476928/how-do-i-think-of-a-representable-functor