Subgroup fully centralized by a category

This article defines a property that can be evaluated for a group of prime power order, equipped with a fusion system
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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 $|C_{P}(R)|\leq |C_{P}(Q)|$ 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.