TITLE: Is Grothendieck classification of tensor norms and Kuratowski's 14 sets theorem somehow related?
QUESTION [19 upvotes]: It is known that there are only 14 reasonable tensor norms in $Ban$. On the other hand it is well known fact for topologists that one can obtain only 14 different sets from a given set  applying closure and complementation operations.
It seems like a pure coincidence but... both constructions starts with the single object (a set/ the injective tensor norm), then apply only predescribed operations (closure and complement/ transpose, dual and right projective associate) and get only 14 different objects in the end.
Is this a simple coincidence or there is something deep behind the scenes? Maybe someone knows other examples?

REPLY [9 votes]: I asked David Sherman this question and this was his response:
In the Kuratowski setup, if you omit complementation, you get 7 elements.  Adding complementation gives you a disjoint upside-down copy.
In the Grothendieck setup, if you omit duality, you get 8 elements (two five-element chains with common inf and sup, like an O).  Adding duality gives you an upside-down copy, but it is not disjoint -- two elements agree between the copies. ''
So, it seems that the answer is NO.