Quiver representations, singularity categories, and monoidal structures

代数的表示从不同的方向进行了研究，涉及monoidal和三角结构。一个目标是描述的发电机和关系表示环和幺半群的投影函子表示的箭。另一个目标是分类厚和局部化的子类别的三角奇异类别。这涉及连续和离散的参数化，反映现有的monoidal或组合结构。奇点范畴的选择是由有限群的表示论、矩阵分解的研究以及代数几何中的应用（包括加权射影线）所激发的。

Representations of algebras are studied from various directions, involving monoidal and triangulated structures. One goal is to describe in terms of generators and relations representation rings and monoids of projections functors for representations of quivers. Another goal is to classify thick and localising subcategories of triangulated singularity categories. This involves continuous and discrete parametrisations, reflecting the existing monoidal or combinatorial structures. The choice of singularity categories is motivated by connections with the representation theory of finite groups, the study of matrix factorisations, and applications in algebraic geometry, including weighted projective lines.