A finite symmetric tensor category over a field 
is a 
-linear abelian rigid symmetric monoidal
category with finite-dimensional morphism spaces, objects
of finite length, finitely many simple objects
up to isomorphism, and enough projectives. Its tensor
product is biexact and the endomorphism ring
of its unit is 
. Rigidity means that every object has a tensor dual. Finite-dimensional
representations of a finite
group give examples, even when the characteristic divides the group
order and the category is not semisimple.
Finite Symmetric Tensor Category
See also
Abelian Category, Fiber Functor, Higher Verlinde Category, Monoidal Category, Tensor CategoryExplore with Wolfram|Alpha
References
Etingof, P.; Gelaki, S.; Nikshych, D.; and Ostrik, V. Tensor Categories. Providence, RI: Amer. Math. Soc., 2015. https://math.mit.edu/~etingof/egnobookfinal.pdf.Cite this as:
Weisstein, Eric W. "Finite Symmetric Tensor Category." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/FiniteSymmetricTensorCategory.html