Relative AR-Correspondence, Co-$t$-Structure and\\ Silting Pair

Abstract:

      As a generalization of tilting pair, which was introduced by Miyashita, the notion of silting pair is introduced in this paper. The authors extend a characterization of tilting modules given by Bazzoni to silting pairs, and prove that there is a one-to-one correspondence between equivalent classes of silting pairs and certain subcategories which satisfy some conditions. Furthermore, the authors also give a bijection between equivalent class of silting pairs and bounded above co-$t$-structure.