The deformation cohomology of a tensor category controls deformations
of its associativity constraint.
Here we deal with the deformation cohomology of tensor categories
generated by one object. In the case when all morphisms are
endomorphisms such categories are completely described by sequences of
algebras (the so-called Schur-Weyl categories).
The deformation complex of a Schur-Weyl category has an explicit
description in terms of the corresponding sequence of algebras.
This approach is convenient for computing the deformation cohomology
of free symmetric tensor categories.
We compare the answers with the exterior invariants of the general
linear Lie algebra.
The results make precise an intriguing connection between the
combinatorics of partitions and invariants of the exterior powers of
the general linear algebra observed by Kostant.
Another example is the Schur-Weyl category of the sequences of
degenerate affine Hecke algebras. The deformation cohomology of this
category coincides with the deformation cohomology of the free
symmetric tensor category of one object with an endomorphism. | 
