Hermitian \(\mathcal{U}\)-theory of exact categories with duality functors (Q1916414)

Let \({\mathcal M}\) be an exact category with a duality functor \(*: {\mathcal M}^{op} \to {\mathcal M}\). Using an analog of Waldhausen's simplicial set approach to \(K\)-theory [cp. \textit{F. Waldhausen}, ``Algebraic \(K\)-theory of spaces'', Lect. Notes Math. 1126, 318-419 (1985; Zbl 0579.18006)] the authors give a new definition of the \({\mathcal U}\)-theory for the category \({\mathcal M}\), defined previously by \textit{M. Uridiya} via the analog of Quillen's \(Q\)-construction [cp. ``\({\mathcal U}\)-theory of exact categories'', Lect. Notes Math. 1437, 303-313 (1990; Zbl 0726.18006)].