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Quadratic functors and metastable homotopy. (English) Zbl 0790.55014
Summary: Quadratic functors lead to the fundamental notion of a quadratic \({\mathcal R}\)-module \(M\) where \({\mathcal R}\) is a ringoid or a ring. We introduce the quadratic tensor product \(A\otimes_{\mathcal R} M\) and the corresponding abelian group \(\operatorname{Hom}_{\mathcal R}(A,M)\) consisting of quadratic forms. Then we describe new quadratic derived functors of \(\otimes\) and Hom together with applications for homotopy groups of Moore spaces and (co)homology groups of Eilenberg-MacLane spaces.

MSC:
55U99 Applied homological algebra and category theory in algebraic topology
18G50 Nonabelian homological algebra (category-theoretic aspects)
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