O2 is a positive allosteric effector (activator) of Hb since the binding of O2 facilitates further binding of O2. In fact, it is 300x easier for the fourth O2 molecule to bind to Hb than for the first.
There are other allosteric effectors of Hb. The molecule 2,3-BPG is a negative allosteric effector (inhibitor). While the four subunits are each in the T state unbound to O2, there is an allosteric site in the middle of them which 2,3-BPG can bind to. Once the first O2 binds to Hb, the site closes up and 2,3-BPG does not bind there anymore. This makes it easier for subsequent O2 molecules to bind to Hb. Conversely, when the first O2 molecule comes off of Hb it makes it easier for 2,3-BPG to bind. When it binds, it shifts the dissociation curve to the right and the affinity for O2 is decreased. So more O2 will come off (dissociate).
As a side note on 2,3-BPG, fetal Hb is comprised of two subunits, alpha and gamma (as opposed to normal adult Hb which is alpha and beta). The molecule 2,3-BPG binds to the beta subunits in adults and spans this gap in the middle of the four subunits. The gamma subunits have a different amino acid in one of the positions with a different charge which makes it very unlikely that 2,3-BPG will attach there. Thus, the dissociation curve shifts way to the left and the affinity of Hb for oxygen goes way up for most partial pressures of O2. This is very important since the fetus wants to pick up as much oxygen from the mother as it can get for itself. If 2,3-BPG were able to bind to fetal Hb then it wouldn't be able to grab as much O2 from the mother.
CO2 is an allosteric inhibitor of Hb. High pH is an allosteric inhibitor of Hb. High temperature is an allosteric inhibitor of Hb (I think... someone check this one).
Cooperativity refers specifically to the fact that when one O2 molecule binds to Hb it induces a conformational change to the Hb molecule which makes it easier for further O2 binding. So the first one helps the second one which helps the third which helps the fourth.
So it's probably a matter of what book you use.