A morphism $f\colon A\to B$ in a 2-category $K$ is said to be (representably) pseudomonic if for all objects $X$, the induced functor
is pseudomonic. In Cat, this is equivalent to $f$ being pseudomonic in the usual sense.
Pseudomonic morphisms may also be called (2,1)-monic and said to make their source into a (2,1)-subobject of their target. See subcategory for discussion.
Of course, any fully faithful morphism is also pseudomonic, and in particular any inverter or equifier is pseudomonic.
Last revised on October 26, 2010 at 18:21:54. See the history of this page for a list of all contributions to it.