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Tensor R-Category

Let R be a commutative ring. A tensor category (C, tensor ,I,a,r,l) is said to be a tensor R-category if C is an R-category and if 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×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

This entry contributed by Christopher Stover

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References

Dieck, T. T. "Quantum Groups and Knot Algebra." 2000. http://www.uni-math.gwdg.de/tammo/dm.pdf.

Cite this as:

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

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