相对于子范畴的同伦分解的存在性  

The Existence of Homotopy Resolutions Relative to the Subcategory

作　　者：马鑫[1] 杨晓燕 Xin MA;Xiao Yan YANG(Center for Quantitative Biology,College of Science,Gansu Agricultural University,Lanzhou 730070,P.R.China;Department of Mathematics,Northwest Normal University,Lanzhou 730070,P.R.China)

机构地区：[1]甘肃农业大学数量生物学研究中心,兰州730070 [2]西北师范大学数学与统计学院,兰州730070

出　　处：《数学学报（中文版）》2020年第1期77-88,共12页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金资助项目(11761060);甘肃省高等学校科研项目(2018B-036)

摘　　要：本文证明了在相对于子范畴的情形下上有界复形的同伦分解的存在性,推广了经典的复形的同伦分解,是使得相对导出范畴具有可操作性的基础.进一步,证明了在R-模范畴和相对于特殊子范畴的情形下,任意无界复形的同伦分解的存在性.最后,建立了同伦范畴和相对导出范畴的(余)局部化序列.Let be a subcategory of an abelian category A.We proceed by generalizing the homotopy resolutions of complexes to the relative version,which is important basis making the relative derived category operational.We prove that every bounded above complex has a dg X resolution.Furthermore,we also show that the existence of resolutions for any unbounded complex when A=R-Mod and is a particular subcategory.Finally,we establish a colocalization sequence of the homotopy category K(A) involving the relative derived category under some condition.

关 键 词：dg X分解 (余)局部化序列 相对导出范畴 

分 类 号：O154.2[理学—数学]