  We show an organized form of quantum de Finetti theorem for Boolean
independence. We define a Boolean analogue of easy quantum groups for the
categories of interval partitions, which is a family of sequences of quantum
semigroups.
  We construct the Haar states on those quantum semigroups. The proof of our de
Finetti theorem is based on the analysis of the Haar states.
  [Modified]Definition of the Boolean quantum semigroups on categories of
interval partitions
  [Delete]Classification of categories of interval partitions
  [Add]Proof of the positiveness of the Haar functionals (in particular they
are Haar states)
