Following the pattern of the Frobenius structure usually assigned
to the 1-dimensional sphere, we investigate the Frobenius
structures of spheres in all other dimensions. Starting from
dimension $d=1$, all the spheres are commutative Frobenius objects
in categories whose arrows are ${(d+1)}$-dimensional cobordisms.
With respect to the language of Frobenius objects, there is no
distinction between these spheres---they are all free of
additional equations formulated in this language. The
corresponding structure makes out of the 0-dimensional sphere not
a commutative but a symmetric Frobenius object.

The talk is based on the paper "Spheres as Frobenius objects",
co-authored with Djordje Baralic and Sonja Telebakovic, which is available
at arxiv.