  The deformation cohomology of a tensor category controls deformations of its
monoidal structure. Here we describe the deformation cohomology of tensor
categories generated by one object (the so-called Schur-Weyl categories). Using
this description we compute the deformation cohomology of free symmetric tensor
categories generated by one object with an algebra of endomorphism free of
zero-divisors. We compare the answers with the exterior invariants of the
general linear Lie algebra.
