Category Theory
In category theory, n-ary functions generalise to n-ary morphisms in a multicategory. The interpretation of an n-ary morphism as an ordinary morphisms whose domain is some sort of product of the domains of the original n-ary morphism will work in a monoidal category. The construction of the derived morphisms of one variable will work in a closed monoidal category. The category of sets is closed monoidal, but so is the category of vector spaces, giving the notion of bilinear transformation above.
Read more about this topic: Binary Function
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