2016/01/07 by Peiyu Zhang, Jiaqun Wei, Zhang, Peiyu +1 · 2 citations
Mathematics · Physics and Astronomy · #13C60 #16D90 #16E05 #16E35 #16G10 #18E30 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #K-Theory and Homology (math.KT) #Nonlinear Waves and Solitons #Representation Theory (math.RT) #Rings and Algebras (math.RA) #math.KT #math.RA #math.RT #msc:13C60 #msc:16D90 #msc:16E05 #msc:16E35 #msc:16G10 #msc:18E30
paper · pdf · doi:10.48550/arxiv.1601.01385
25 pages
arxiv created 2016/01/07 · openalex publication_date 2016/01/07 · arxiv updated 2016/01/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce and study the new concepts of cosilting complexes, cosilting modules and AIR-cotilting modules. We prove that the three concepts AIR-cotilting modules, cosilting modules and quasi-cotilting modules coincide with each other, in contrast with the dual fact that AIR-tilting modules, silting modules and quasi-tilting modules are different. Further, we show that there are bijections between the following four classes (1) equivalent classes of AIR-cotilting (resp., cosilting, quasi-cotilting) modules, (2) equivalent classes of 2-term cosilting complexes, (3) torsion-free cover classes and (4) torsion-free special precover classes. We also extend a classical result of Auslander and Reiten on the correspondence between certain contravariantly finite subcategories and cotilting modules to the case of cosilting complexes.