Pairwise compatibility for 2-simple minded collections

摘要: Abstract In τ-tilting theory, it is often difficult to determine when a set of bricks forms 2-simple minded collection. The aim this paper contained in collection for finite algebra. We begin by extending the definition mutation from collections more general sets (which we call semibrick pairs). This gives us an algorithm check if pair then use show that gentle algebra (whose quiver contains no loops or 2-cycles) are given pairwise compatibility conditions and only every vertex corresponding has degree at most 2. As application, classifying space τ-cluster morphism category Eilenberg-MacLane