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Tensor R-Category

A tensor R-category, for a commutative ring R, is a tensor category (C, tensor ,I,a,r,l) such that C is an R-category and the tensor product functor is an R-bilinear map

Hom(A,B)×Hom(C,D)->Hom(A tensor C,B tensor D)

on sets of morphisms defined by (f,g)|->f tensor g.

See also

Category, Category Theory, Functor, Hom-Set, Morphism, Natural Isomorphism, Natural Transformation, Object, R-Category, R-Module, Strict Tensor Category, Unital Natural Transformation

Portions of this entry contributed by Christopher Stover

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References

tom Dieck, T. "Quantum Groups and Knot Algebra." May 4, 2004. https://www.uni-math.gwdg.de/tammo/dm.pdf.

Referenced on Wolfram|Alpha

Tensor R-Category

Cite this as:

Weisstein, Eric W., with contributions by Christopher Stover. "Tensor R-Category." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/TensorR-Category.html

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