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From: Robin Houston <r.houston@cs.man.ac.uk>
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Subject: Full and faithful
Date: Fri, 30 Mar 2007 18:44:37 +0100
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A functor F: C -> D is full and faithful just when, for all
categories X and functors G, H: X -> C, the whiskering action of F
induces a bijection between [G, H] and [FG, FH]  (where [G, H]
denotes the set of natural transformations from G to H).

Clearly this formulation makes sense in any bicategory. Is there a
name for 1-cells with this property?

Thanks!

Robin