  Let p be a prime number and G a finite group of order divisible by p. Quillen
showed that the Brown poset of nonidentity p-subgroups of G is homotopy
equivalent to its subposet of nonidentity elementary abelian subgroups. We show
here that a similar statement holds for the fusion category of nonidentity
p-subgroups of G. Other categories of p-subgroups of G are also considered.
