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 $$P$$.