共查询到19条相似文献,搜索用时 62 毫秒
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函子范畴是—类重要的范畴,因为许多常见的范畴都是函子范畴,并且任意给定的范畴都可以通过Yoneda引理嵌入到一个函子范畴,而函子范畴具有比原范畴更好的性质。本文证明了Abel范畴的recollement可以自然诱导两类函子范畴的recollment.应用到k-线性范畴,得到k.线性Abel范畴的recollement可以自然诱导其模范畴的recollement. 相似文献
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从三角范畴的recollement到Abel范畴的recollement 总被引:1,自引:0,他引:1
研究了三角范畴的recollement与Abel范畴的recollement的关系.证明了:若三角范畴D允许关于三角范畴D和D的recollement,则Abel范畴D/T允许关于Abel范畴D/i^*(T)和D/j^*(T)的recollement,其中T为D的cluster-倾斜子范畴,且满足i*i^*(T)*T,j^*j^*(T)^*T. 相似文献
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文章研究了三角范畴D及其coherent函子范畴A(D)的recollement之间的关系.利用D的recollement可以诱导A(D)的prerecollement,文章证明了该prerecollement是recollement的充分必要条件是D的recollement是可裂的;并且D的recollement可以诱导A(D)的prerecollement. 相似文献
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在外三角范畴中,本文引入同调系统Θ(又称为Θ-系统)的概念,此概念统一了模范畴的分层系统和三角范畴的同调系统.本文证明了一个Θ-系统能够唯一地确定一个Θ-投射系统.给定一个Θ-投射系统(Θ, Q,≤),本文也证明了滤链多样性不依赖于滤链的选择,建立了所有Θ-滤对象构成的子范畴■(Θ)和模范畴mod(B)中的所有?-好模构成的子范畴之间的同构,其中B是标准分层代数. 相似文献
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We generalize results on existence of recollement situations of singularity categories of lower triangular Gorenstein algebras and stable monomorphism categories of Cohen–Macaulay modules. 相似文献
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设{D',D,D'';i^*,i*=i!,i^!,j!,j^*=j^!,j*)是一个recollement,本文证明了当D有AR-三角时,D',D''也有AR-三角,并且它们的AR-三角完全可由D中AR-三角诱导. 相似文献
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A notion of mutation of subcategories in a right triangulated category is defined in this article. When (𝒵, 𝒵) is a 𝒟-mutation pair in a right triangulated category 𝒞, the quotient category 𝒵/𝒟 carries naturally a right triangulated structure. Moreover, if the right triangulated category satisfies some reasonable conditions, then the right triangulated quotient category 𝒵/𝒟 becomes a triangulated category. When 𝒞 is triangulated, our result unifies the constructions of the quotient triangulated categories by Iyama-Yoshino and by Jørgensen, respectively. 相似文献
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作者在弱幂等完备的正合范畴(A,E)中引入了复形的新的定义,并且证明了E-正合复形的同伦范畴Kex(E)是同伦范畴KE(A)的厚子范畴.给定(A,E)中的余挠对(x,y),定义了正合范畴(CE(A),C(E))中的两个余挠对((x)E,dg(y)E)和(dg(x)E,(y)E),并且证明了当A是可数完备时,CE(A)中... 相似文献
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《代数通讯》2013,41(2):843-858
Abstract We study the Morita-Takeuchi context connecting two coalgebras which is dual to the Morita context for algebras. We show that every Morita-Takeuchi context, connecting two coalgebras C and D, leads to an equivalence between quotient categories of the comodule categories C M and D M. Afterwards we introduce a special Morita-Takeuchi context, called closed, and show that there is a bijection between isomorphism types of closed contexts and isomorphism types of category equivalences between quotient categories of C M and D M determined by localizing subcategories. This represents a dualization of the classical Morita theorems. Finally we show that from every general context one can construct a closed one. 相似文献
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We study the problem of lifting and restricting TTF triples (equivalently, recollement data) for a certain wide type of triangulated
categories. This, together with the parametrizations of TTF triples given in Nicolás and Saorín (Parametrizing recollement
data for triangulated categories. To appear in J. Algebra), allows us to show that many well-known recollements of right bounded
derived categories of algebras are restrictions of recollements in the unbounded level, and leads to criteria to detect recollements
of general right bounded derived categories. In particular, we give in Theorem 1 necessary and sufficient conditions for a
right bounded derived category of a differential graded (=dg) category to be a recollement of right bounded derived categories of dg categories.
Theorem 2 considers the case of dg categories with cohomology concentrated in non-negative degrees. In Theorem 3 we consider
the particular case in which those dg categories are just ordinary algebras. 相似文献
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The results of [7] and [2] gave a recursive construction for all quasi-hereditary and standardly stratified algebras starting with local algebras and suitable bimodules. Using the notion of stratifying pairs of subcategories, introduced in [3], we generalize these earlier results to construct recursively all CPS-stratified algebras. 相似文献
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Let 𝒳 ? 𝒜 be subcategories of a triangulated category 𝒯, and 𝒳 a functorially finite subcategory of 𝒜. If 𝒜 has the properties that any 𝒳-monomorphism of 𝒜 has a cone and any 𝒳-epimorphism has a cocone, then the subfactor category 𝒜/[𝒳] forms a pretriangulated category in the sense of [4]. Moreover, the above pretriangulated category 𝒜/[𝒳] with 𝒯(𝒳, 𝒳[1]) = 0 becomes a triangulated category if and only if (𝒜, 𝒜) forms an 𝒳-mutation pair and 𝒜 is closed under extensions. 相似文献