同伦范畴中recollement的建立
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摘要
证明了在相对情形下上有界复形的同伦分解的存在性,是对经典复形的同伦分解的推广.建立了同伦范畴K(A)和相对导出范畴DX(A)的左recollement.证明了dg X和DX(A)是三角等价的,其中X是A的反变有限的容许子范畴.
The paper studied the existence of homological resolutions of bounded above complexes in the relative case, which was a generalization of the usual homological resolutions. The left recollement of the homotopic category K(A) and the relative derived category DX(A) was built. We gave a trianglated equivalence between the dg X and DX(A), where X was contravariantly finite and admissible subcategory of A.
The paper studied the existence of homological resolutions of bounded above complexes in the relative case, which was a generalization of the usual homological resolutions. The left recollement of the homotopic category K(A) and the relative derived category DX(A) was built. We gave a trianglated equivalence between the dg X and DX(A), where X was contravariantly finite and admissible subcategory of A.
引文
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[2] Keller B. Derived categories and their uses[M]//Handbook of Algebra Vol.1, Amsterdam:North-Holland Publishing Co, 1996.
[3] Asadollahi J, Hafezi R. On relative derived categories[J].Communications in Algebra, 2016, 44(12):5454-5477.
[4]章璞.三角范畴与导出范畴[M].北京:科学出版社,2015.
[5] Verdier J L. Des catégories dérivées abéliennes, Astrisque239[M]. Pairs:Societ Mathematique de France, 1996.
[6] Bravo D, Gillespie J, Hovey M. The stable module category of a general ring[EB/OL].[2014-05-23]. https://arxiv.org/pdf/1405.5768.pdf.
[7] Enochs E E, López-ramos J A. Kaplansky classes[J].Rend Sem Mat Univ Padova, 2002, 107(5):67-79.
[8] Gillespie J. Model structures on modules over Ding-chen rings[J]. Homology, Homotopy and Applications, 2010,12(1):61-73.
[2] Keller B. Derived categories and their uses[M]//Handbook of Algebra Vol.1, Amsterdam:North-Holland Publishing Co, 1996.
[3] Asadollahi J, Hafezi R. On relative derived categories[J].Communications in Algebra, 2016, 44(12):5454-5477.
[4]章璞.三角范畴与导出范畴[M].北京:科学出版社,2015.
[5] Verdier J L. Des catégories dérivées abéliennes, Astrisque239[M]. Pairs:Societ Mathematique de France, 1996.
[6] Bravo D, Gillespie J, Hovey M. The stable module category of a general ring[EB/OL].[2014-05-23]. https://arxiv.org/pdf/1405.5768.pdf.
[7] Enochs E E, López-ramos J A. Kaplansky classes[J].Rend Sem Mat Univ Padova, 2002, 107(5):67-79.
[8] Gillespie J. Model structures on modules over Ding-chen rings[J]. Homology, Homotopy and Applications, 2010,12(1):61-73.