nLab
conjugation action

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 $g\in G$

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

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

Definition

For infinity-actions see at infinity-action – Conjugation action

Related concepts

• adjoint action