Subgroup fully normalized by a category

Definition
Suppose $$P$$ is a group of prime power order and $$\mathcal{F}$$ is a category on $$P$$. A subgroup $$R$$ of $$P$$ is termed fully normalized by $$\mathcal{F}$$ if, for any $$Q \le P$$ such that $$Q$$ and $$R$$ are isomorphic via $$\mathcal{F}$$, $$|N_P(Q)| \le |N_P(R)|$$.

The definition is typically used when $$\mathcal{F}$$ is a fusion system on $$P$$.