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Is there an easy way to characterize pseudo split epimorphisms in Cat?

Obs: A pseudo split epimorphism in Cat is a functor $F: E\to B $ such that there is a functor $ M: B\to E $ and a natural isomorphism $\alpha : FM\to Id _ B $.

Thank you in advance

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    $\begingroup$ What kind of characterization are you looking for? The definition is pretty easy as it is. $\endgroup$
    – Tilman
    Jul 19, 2014 at 18:54
  • $\begingroup$ Sorry for delaying. I was looking for something easily verifiable. Like "the monomorphisms are the faithful embeddings" . Or like the following article: mat.uc.pt/preprints/ps/p0116.ps $\endgroup$
    – Fernando
    Jul 27, 2014 at 2:09

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