JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2020, Vol. 55 ›› Issue (12): 97-102.doi: 10.6040/j.issn.1671-9352.0.2020.194

Previous Articles    

A new construction method of triangulated model structures

ZHANG Ping-er, YANG Xiao-yan   

  1. College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China
  • Published:2020-12-01

PDF (PC)

322

Abstract: Let T be a triangulated category and ξ denote some proper class of triangles, and suppose that we have two complete hereditary cotorsion pairs(Q,R)and(Q,R)with respect to ξ in T satisfying R⊆R and Q ∩R=Q∩R. We show how to construct an unique triangulated model structures with respect to ξ on T with Q(resp.Q)as the class of cofibrant(resp. trivially cofibrant)objects and R(resp. R)as the class of fibrant(resp. trivially fibrant)objects.

Key words: triangulated category, complete hereditary cotorsion pair, thick class, Hovey triple

CLC Number: 

  • O154.2
[1] YANG Xiaoyan. Model structures on triangulated categories[J]. Glasgow Math J, 2015, 57:263-284.
[2] BECKER H. Models for singularity categories[J]. Adv Math, 2014, 254:187-232.
[3] GILLESPIE J. Gorenstein complexes and recollements from cotorsion pairs[J]. Adv Math, 2016, 291:265-306.
[4] GILLESPIE J. Hereditary abelian model categories[J]. Bull London Math Soc, 2016, 48:895-922.
[5] VERDIER J L. Catégories dérivées[M] //Lecture Notes in Math, Vol. 569. Berlin: Springer-Verlag, 1977: 262-311.
[6] BELIGIANNIS A. Relative homological algebra and purity in triangulated categories[J]. J Algebra, 2000, 227(1):268-361.
[7] ASADOLLAHI J, SALARIAN S. Gorenstein objects in triangulated categories[J]. J Algebra, 2004, 281:264-286.
[1] ZHENG Min, CHEN Qing-hua. Ki-group of t-structure of triangulated category [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2020, 55(8): 48-53.
[2] YANG Ting, XIE Yun-li. Higher rigid subcategories and t-structures [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2020, 55(12): 69-75.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
No Suggested Reading articles found!
Copyright 2018 © Editorial office of JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)
Supported by Beijing Magtech Co.Ltd