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).

Last revised on March 13, 2012 at 01:50:13.
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