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 $P$.