Addendum and Erratum: Mapping cones for morphisms involving a band complex in the bounded derived category of a gentle algebra

Abstract

In this note we correct two oversights in [Mapping cones in the bounded derived category of a gentle algebra, J. Algebra 530 (2019), which only occur when a band complex is involved. As a consequence we see that the mapping cone of a morphism between two band complexes can decompose into arbitrarily many indecomposable direct summands.