We give a finite combinatorial test for finite seminormal functors to possess the property O n and use it in establishing that in some cases this property leads to some well-known functors. For example, if some functor F possesses the property O 2 then F 2 coincides with either exp 2 or the squaring functor. Hence we conclude that if F (D ω1 ) and D ω1 are homeomorphic then F 2 is either exp 2 or (·) 2 .
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