Categorical and simplicial constructions and dualization in algebraic K-theory
There are several ways to construct the algebraic \(K\)-theory of an exact category \(\mathcal A\). A construction \(T\) is called self-dual if there are good isomorphisms between \(T(\mathcal A)\) and \(T({\mathcal A}^{\text{op}})\). The author describes the extent to which various already known constructions are self-dual. In particular the Gillet-Grayson \(G\)-construction is not self-dual, but the author obtains a new self-dual construction \(W({\mathcal A})\) by combining \(G({\mathcal A})\) and \(G({\mathcal A}^{\text{op}})\). When \({\mathcal A}\) is an exact category with duality, he uses \(W({\mathcal A})\) to describe the duality automorphism of \(K_1({\mathcal A})\) in terms of double exact sequences.
scientific article; zbMATH DE number 1785681