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2006•Journal of MathematicsRequires access

A REPRESENTATION OF ADDITIVE FUNCTORS OVER FUNCTOR CATEGORIES

Kuang Min

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Abstract

We study the representation of additive functors over the functor category Mod C,convert an Abel group into a left C-module in Mod C,construct a Hom functor and a functorial morphism, and prove that any contravariant left exact additive functor F:Mod C→Ab converting sums to products is equivalent to some Hom functor.The results obtained here generalize the Watts theorem to functor categories.

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What this paper is about

We study the representation of additive functors over the functor category Mod C,convert an Abel group into a left C-module in Mod C,construct a Hom functor and a functorial morphism, and prove that any contravariant left exact additive functor F:Mod C→Ab converting sums to products is equivalent to some Hom functor.The results obtained here generalize the Watts theorem to functor categories.

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Available abstract

We study the representation of additive functors over the functor category Mod C,convert an Abel group into a left C-module in Mod C,construct a Hom functor and a functorial morphism, and prove that any contravariant left exact additive functor F:Mod C→Ab converting sums to products is equivalent to some Hom functor.The results obtained here generalize the Watts theorem to functor categories.

Key concepts: Functor, Mathematics, Morphism, Covariance and contravariance of vectors, Exact functor, Pure mathematics, Natural transformation, Functor category

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