# nLab conjugation action

### Context

#### Algebra

higher algebra

universal algebra

# Contents

## Idea

For $G$ a group and $V_1$ and $V_2$ two objects equipped with $G$-action, the conjugation action on morphisms $f : V_1 \to V_2$ (not necessarily respecting the $G$-action) is for $g \in G$

$f \mapsto g \circ f \circ g^{-1} \,.$

The invariants? of the conjugation action are the $G$-action homomorphism.

## Definition

Revised on November 4, 2014 19:08:55 by Urs Schreiber (141.0.8.155)