Semibrick-cosilting correspondence

Abstract

Let (Formula presented.) be a finite-dimensional algebra. In this paper, we show that there is a natural bijection between cosilting modules in (Formula presented.) and semibricks in (Formula presented.) satisfying some condition. Also this bijection restricts to a bijection between all semibricks in (Formula presented.) and a certain subclass of cosilting modules. These bijections are generalizations of Asai's correspondence (Int. Math. Res. Not. 16 (2020) 4993–5054) between support (Formula presented.) -tilting modules and right finite semibricks. © 2025 The Author(s). The publishing rights in this article are licensed to the London Mathematical Society under an exclusive licence.