Higher K-theory of forms II. From exact categories to chain complexes

Abstract

We prove basic statements about the Hermitian K-theory of exact form categories with weak equivalences. Notably, we extend a quadratic functor with values in abelian groups from an exact category to its category of bounded chain complexes in a way that does not change Grothendieck-Witt spaces. This is used in joint work with Marlowe for the comparison of the classical 1-categorical version of the Hermitian K-theory of exact categories with the infinity-categorical version of Calmes-Dotto-Harpaz-Hebestreit-Land-Moi-Nardin-Nikolaus-Steimle.