A note on the Schur multiplier of a fusion system

The Schur multiplier of a fusion system on a finite p-group P, being defined as the inverse limit of the Schur multipliers of the subgroups of P taken over the category , has a series of properties analogous to some properties of Schur multipliers of finite groups. This is one of the tools used in [R. Kessar, The Solomon system does not occur as fusion system of a 2-block, preprint, 2004] to show that the Solomon fusion system cannot arise as the Brauer category of a p-block of a finite group.