Abstract
Quadratic functors lead to the fundamental notion of a quadratic R -module M where R is a ringoid or a ring. We introduce the quadratic tensor product A ⊗ R M and the corresponding abelian group Hom R ( A,M) consisting of quadratic forms. Then we describe new quadratic derived functors of ⊗ and Hom together with applications for homotopy groups of Moore spaces and (co)homology groups of Eilenberg-Mac Lane spaces.
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