The deformation cohomology of a free symmetric tensor category generated by one object is the exterior algebra on odd-degree generators e_1, e_3, e_5, ..., with deg(e_{2i-1}) = 2i-1.
Davydov, Twisting of monoidal structures
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Deformation cohomology of Schur-Weyl categories. Free symmetric categories
The deformation cohomology of a free symmetric tensor category generated by one object is the exterior algebra on odd-degree generators e_1, e_3, e_5, ..., with deg(e_{2i-1}) = 2i-1.