The 2-group of symmetries of a split chain complex

We explicitly compute the 2-group of self-equivalences and (homotopy classes of) chain homotopies between them for any split chain complex A in an arbitrary K-linear abelian category (K any commutative ring with unit). In particular, it is shown that it is a split 2-group whose equivalence class depends only on the homology of A, and that it is equivalent to the trivial 2-group when A is exact. This provides a description of the general linear 2-group of a Baez and Crans 2-vector space over an arbitrary field F and of its generalization to chain complexes of vector spaces of arbitrary length.