# nLab faithful morphism

### Context

#### 2-Category theory

2-category theory

## Definition

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

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

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

## Remarks

Revised on April 26, 2016 11:31:45 by Mike Shulman (76.167.222.204)