# nLab faithful morphism

2-category theory

## Definition

A morphism $f:A\to B$ in a 2-category $K$ is said to be (representably) faithful if for all objects $X$, the induced functor

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

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

## Remarks

Revised on May 21, 2010 19:14:45 by Mike Shulman (128.192.37.11)