A semigroup with zero is idempotent bounded (IB) if it is the 0-direct
union of idempotent generated principal left ideals and the 0-direct
union of idempotent generated principal right ideals. Notable examples
are completely 0-simple semigroups and the wider class of primitive a
bundant semigroups. Significant to the structure of these semigroups i
s that they are all categorical at zero. In this paper we describe IB
semigroups that are categorical at zero in terms of double blocked Ree
s matrix semigroups. This generalises Fountain's characterisation of p
rimitive abundant semigroups via blocked Rees matrix semigroups [1], w
hich in turn yields the Rees theorem for completely 0-simple semigroup
s.