  After a brief survey of the basic definitions of the Grothendieck--Verdier
categories and dualities, I consider in this context introduced earlier
dualities in the categories of quadratic algebras and operads, largely
motivated by the theory of quantum groups. Finally, I argue that Dubrovin's
"almost duality" in the theory of Frobenius manifolds and quantum cohomology
also must fit a (possibly extended) version of Grothendieck--Verdier duality.
