  We construct the spin foam model for N=2 supergravity in three dimensions.
Classically, it is a BF theory with gauge algebra osp(2|2). This algebra has
representations which are not completely reducible. This complicates the
procedure when building a state sum. Fortunately, one can and should excise
these representations. We show that the restricted subset of representations
form a subcategory closed under tensor product. The resulting state-sum is once
again a topological invariant. Furthermore, within this framework one can
identify positively and negatively charged fermions propagating on the spin
foam. These results on osp(2|2) representations and intertwiners apply more
generally to spin network states for N=2 loop quantum supergravity (in 3+1
dimensions) where it allows to define a notion of BPS states.
