2000/05/17 by Mitsuo Hoshino, Yoshiaki Kato, Hoshino, Mitsuo +3 · 1 citation
Mathematics · #16G99 #16S90 #18E30 #18E40 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT) #Rings and Algebras (math.RA) #math.RA #math.RT #msc:16G99 #msc:16S90 #msc:18E30 #msc:18E40
paper · pdf · doi:10.48550/arxiv.math/0005172
17 pages, AMSLaTeX
arxiv created 2000/05/17 · openalex publication_date 2000/05/17 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
First, we show that a compact object C in a triangulated category, which satisfies suitable conditions, induces a t-structure. Second, in an abelian category we show that a complex P\centerdot of small projective objects of term length two, which satisfies suitable conditions, induces a torsion theory. In the case of module categories, using a torsion theory, we give equivalent conditions for P\centerdot to be a tilting complex. Finally, in the case of artin algebras, we give one to one correspondence between tilting complexes of term length two and torsion theories with certain conditions.