共查询到20条相似文献,搜索用时 31 毫秒
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Theo Bühler 《Expositiones Mathematicae》2010,28(1):1-69
We survey the basics of homological algebra in exact categories in the sense of Quillen. All diagram lemmas are proved directly from the axioms, notably the five lemma, the 3×3-lemma and the snake lemma. We briefly discuss exact functors, idempotent completion and weak idempotent completeness. We then show that it is possible to construct the derived category of an exact category without any embedding into abelian categories and we sketch Deligne's approach to derived functors. The construction of classical derived functors with values in an abelian category painlessly translates to exact categories, i.e., we give proofs of the comparison theorem for projective resolutions and the horseshoe lemma. After discussing some examples we elaborate on Thomason's proof of the Gabriel–Quillen embedding theorem in an appendix. 相似文献
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Pierre Baumann 《Advances in Mathematics》2011,(5):2874
Let U be the enveloping algebra of a symmetric Kac–Moody algebra. The Weyl group acts on U, up to a sign. In addition, the positive subalgebra U+ contains a so-called semicanonical basis, with remarkable properties. The aim of this paper is to show that these two structures are as compatible as possible. 相似文献
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We prove that the 2-category of small abelian categories with exact functors is anti-equivalent to the 2-category of definable additive categories. We define and compare sheaves of localisations associated to the objects of these categories. We investigate the natural image of the free abelian category over a ring in the module category over that ring and use this to describe a basis for the Ziegler topology on injectives; the last can be viewed model-theoretically as an elimination of imaginaries result. 相似文献
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Paul Balmer 《Advances in Mathematics》2011,(5):4352
We prove that the category of modules over a separable ring object in a tensor triangulated category admits a unique structure of triangulated category which is compatible with the original one. This applies in particular to étale algebras. More generally, we do this for exact separable monads. 相似文献
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James Gillespie 《Journal of Pure and Applied Algebra》2011,215(12):2892-2902
We define model structures on exact categories, which we call exact model structures. We look at the relationship between these model structures and cotorsion pairs on the exact category. In particular, when the underlying category is weakly idempotent complete, we get Hovey’s one-to-one correspondence between model structures and complete cotorsion pairs. We classify the right and the left homotopy relation in terms of the cotorsion pairs and look at examples of exact model structures. In particular, we see that given any hereditary abelian model category, the full subcategories of cofibrant, fibrant and cofibrant-fibrant subobjects each has natural exact model structures equivalent to the original model structure. These model structures each has interesting characteristics. For example, the cofibrant-fibrant subobjects form a Frobenius category, whose stable category is the same as the homotopy category of its model structure. 相似文献
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We investigate a non-simply-laced version of cluster structures for 2-Calabi–Yau or stably 2-Calabi–Yau categories over arbitrary fields. It results that 2-Calabi–Yau or stably 2-Calabi–Yau categories having a cluster tilting subcategory with neither loops nor 2-cycles do have the generalized version of cluster structure. This is in particular the case of cluster categories over non-algebraically closed fields. 相似文献
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《Quaestiones Mathematicae》2013,36(5):623-629
AbstractWe present a new admissibility theorem for Galois structures in the sense of G. Janelidze. It applies to relative exact categories satisfying a suitable relative modularity condition, and extends the known admissibility theorem in the theory of generalized central extensions. We also show that our relative modularity condition holds in every relative exact Goursat category. 相似文献
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We introduce the notion of a definable category–a category equivalent to a full subcategory of a locally finitely presentable category that is closed under products, directed colimits and pure subobjects. Definable subcategories are precisely the finite-injectivity classes. We prove a 2-duality between the 2-category of small exact categories and the 2-category of definable categories, and provide a new proof of its additive version. We further introduce a third vertex of the 2-category of regular toposes and show that the diagram of 2-(anti-)equivalences between three 2-categories commutes; the corresponding additive triangle is well-known. 相似文献
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Marco Schlichting 《Topology》2004,43(5):1089-1103
We generalize, from additive categories to exact categories, the concept of “Karoubi filtration” and the associated homotopy fibration in algebraic K-theory. As an application, we construct for any idempotent complete exact category an exact category such that . 相似文献
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We introduce notions of finiteness obstruction, Euler characteristic, L2-Euler characteristic, and Möbius inversion for wide classes of categories. The finiteness obstruction of a category Γ of type (FPR) is a class in the projective class group K0(RΓ); the functorial Euler characteristic and functorial L2-Euler characteristic are respectively its RΓ-rank and L2-rank. We also extend the second author's K-theoretic Möbius inversion from finite categories to quasi-finite categories. Our main example is the proper orbit category, for which these invariants are established notions in the geometry and topology of classifying spaces for proper group actions. Baez and Dolan's groupoid cardinality and Leinster's Euler characteristic are special cases of the L2-Euler characteristic. Some of Leinster's results on Möbius–Rota inversion are special cases of the K-theoretic Möbius inversion. 相似文献
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J.M. Casas N. Inassaridze E. Khmaladze M. Ladra 《Journal of Pure and Applied Algebra》2005,200(3):3037-280
The tripleability of the category of crossed n-cubes is studied. The leading cotriple homology of these homotopy (n+1)-types is investigated, describing it as Hopf type formulas. 相似文献
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Geoffrey M.L. Powell 《Journal of Pure and Applied Algebra》2010,214(8):1435-1449
The calculation of the iterated loop functors and their left derived functors on the category of unstable modules over the Steenrod algebra is a non-trivial problem; Singer constructed an explicit and functorial chain complex to calculate these functors. The results of Singer are analysed to give information on the behaviour of these functors with respect to the nilpotent filtration of the category of unstable modules.We show that, if an unstable module M supports an action of an unstable algebra K, then the derived functors of the iterated loop functors applied to M support actions of iterated doubles of K. This allows the finiteness results of Henn on unstable modules which support actions of unstable algebras to be applied to deduce structural results on the derived functors of iterated loops on such modules. 相似文献
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We study the relative homological behaviour of the omnipresent class of cleft extensions of abelian categories. This class of extensions is a natural generalization of the trivial extensions studied in detail by Fossum, Griffith and Reiten and by Palmer and Roos. We apply our results to the relative homology of cleft extensions of rings. 相似文献
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Fabrizio Durante Piotr Jaworski Radko Mesiar 《Statistics & probability letters》2011,81(12):1995-2003
We consider a family of copulas that are invariant under univariate truncation. Such a family has some distinguishing properties: it is generated by means of a univariate function; it can capture non-exchangeable dependence structures; it can be easily simulated. Moreover, such a class presents strong probabilistic similarities with the class of Archimedean copulas from a theoretical and practical point of view. 相似文献
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We investigate the splitting of short exact sequences of the form
0→X→Y→E→0, 相似文献
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Kenneth S. Berenhaut John V. Baxley Robert G. Lyday 《Statistics & probability letters》2011,81(12):1940-1944
In this note, we consider a question of Móri regarding estimating the deviation of the kth terms of two discrete probability distributions in terms of the supremum distance between their generating functions over the interval [0,1]. An optimal bound for distributions on finite support is obtained. Properties of Chebyshev polynomials are employed. 相似文献