Subgroup fully centralized by a category

Definition
Suppose $$P$$ is a group of prime power order and $$\mathcal{F}$$ is a category on $$P$$. A subgroup $$Q$$ of $$P$$ is said to be fully centralized by $$\mathcal{F}$$ if $$|C_P(R)| \le |C_P(Q)|$$ for all subgroups $$R$$ of $$P$$ that are isomorphic to $$Q$$ in $$\mathcal{F}$$.

The term is typically used when $$\mathcal{F}$$ is a fusion system.