Fusion subsystem

Definition

Suppose $P$ is a group of prime power order and $\mathcal{F}$ is a fusion system on $P$. In other words, $\mathcal{F}$ is a category on $P$ satisfying the conditions necessary for a fusion system. Then, a fusion subsystem or subfusion system of $\mathcal{F}$ is a subcategory of $\mathcal{F}$ that is a fusion system on some subgroup $Q$ of $P$.