If $K$ has finite limits and $f:A\to B$ is eso, then for any $Z$ the functor $K(B,Z)\to K(A,Z)$ is faithful and conservative.

If $K$ is a 1-category with finite limits, regarded as a 2-category with only identity 2-cells, then a morphism in $K$ is eso if and only if it is an extremal epimorphism (equivalently, a strong epimorphism).

Revised on March 13, 2012 01:50:13
by Toby Bartels
(75.88.85.16)