Estruturas trianguladas em quocientes da categoria de Bondarenko

Abstract

In 2003, V. Bekkert and H. Merklen introduced the Bondarenko category with the aim of classifying indecomposable objects in the derived category of Gentle algebras. Subsequently, A. Franco, H. Giraldo, and P. Rizzo applied similar techniques in the case of SUMP algebras. In the current study, we have conducted research on the Bondarenko category. We demonstrate that a specific quotient of this cate- gory possesses a triangular structure. Furthermore, we establish a connection between triangles in the homotopy category of projectives of a SUMP algebra and triangles in a particular quotient of the Bondarenko category associated with the same SUMP algebra.