Categories with a conjugation and a commuting duality yield an 8-periodic chain complex of Witt groups, exact for artinian abelian categories or categories with semilocal rad-adically complete endomorphism algebras.
Pfister:Quadratische Formen in beliebigen K¨ orper, Invent
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Categories with conjugation and octagons of Witt groups
Categories with a conjugation and a commuting duality yield an 8-periodic chain complex of Witt groups, exact for artinian abelian categories or categories with semilocal rad-adically complete endomorphism algebras.