Categorical and simplicial constructions and dualization in algebraic K-theory, by Alexander Nenashev

Given an exact category A, we introduce a bisimplicial set WA which is self-dual and contains both the G-construction of A and its dualization. We prove that the embeddings of G.A and G^{op}.A into WA are homotopy equivalences. If A is an exact category with duality, we calculate the induced action of duality on K_1(A). We also survey on the self-duality property of some known constructions.


Alexander Nenashev <nenashev@lychee.math.nus.edu.sg>