nLab pseudomonic morphism

Definition

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

$$K(X,A) \to K(X,B)$$

is pseudomonic. In Cat, this is equivalent to $f$ being pseudomonic in the usual sense.

Remarks

• 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.

Related pages

• subcategory
• fully faithful morphism
• conservative morphism
• faithful morphism