We provide, explicitly, equivalences and dual equivalences between categories of abstract quadratic forms theories and subcategories of multifields and multirings, that will bring new perspectives and methods to the abstract theories of quadratic forms in forthcoming papers.

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We register, explicitly, equivalences and dual equivalences between categories of abstract quadratic forms theories and (sub)categories of multirings and multifields. Multigroups and MultiringsThis section is a compiled o basic definitions and results included for the convenience of the reader. For more details, consult [6].Multigroups are a generalization of groups. We can think that a multigroup is a group with a multivalued operation: Definition 1.1 A multigroup is a quadruple (G, * , r, 1), where G is a non-empty set,