# nLab conservative morphism

### Context

#### 2-Category theory

2-category theory

# Contents

## Definition

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

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

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

## Remarks

Revised on March 9, 2012 20:20:51 by Urs Schreiber (82.113.106.131)