کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4595927 | 1336141 | 2015 | 27 صفحه PDF | دانلود رایگان |

We study the behavior of direct limits in the heart of a t-structure. We prove that, for any compactly generated t-structure in a triangulated category with coproducts, countable direct limits are exact in its heart. Then, for a given Grothendieck category GG and a torsion pair t=(T,F)t=(T,F) in GG, we show that the heart HtHt of the associated t-structure in the derived category D(G)D(G) is AB5 if, and only if, it is a Grothendieck category. If this is the case, then FF is closed under taking direct limits. The reverse implication is true for a wide class of torsion pairs which include the hereditary ones, those for which TT is a cogenerating class and those for which FF is a generating class. The results allow to extend results by Buan–Krause and Colpi-Gregorio to the general context of Grothendieck categories and to improve some results of (co)tilting theory of modules.
Journal: Journal of Pure and Applied Algebra - Volume 219, Issue 9, September 2015, Pages 4117–4143