Results 161 to 170 of about 29,359 (208)

Derived Equivalences As Derived Functors

Journal of the London Mathematical Society, 1991
In [J. Lond. Math. Soc., II. Ser. 39, No.3, 436-456 (1989; Zbl 0642.16034)], we proved that two algebras \(\Lambda\) and \(\Gamma\) are ``derived equivalent'', meaning that the derived category of modules for \(\Lambda\) is equivalent to that for \(\Gamma\), precisely when \(\Gamma\) is isomorphic to the endomorphism ring of what we called a ``tilting ...
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Relative weak derived functors

Commentationes Mathematicae Universitatis Carolinae, 2020
Summary: Let \(R\) be a ring, \(n\) a fixed non-negative integer, \(\mathscr{WI}\) the class of all left \(R\)-modules with weak injective dimension at most \(n\), and \(\mathscr{WF}\) the class of all right \(R\)-modules with weak flat dimension at most \(n\).
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Derived Functor SemiTor

2010
A complex C• over an exact category [28] A is called exact if it is composed of exact triples Zi → Ci → Zi+1 in A. A complex over A is called acyclic if it is homotopy equivalent to an exact complex (or equivalently, if it is a direct summand of an exact complex).
Leonid Positselski, Sergey Arkhipov, Dmitriy Rumynin   +2 more
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Derived Functor SemiExt

2010
Let A be an exact category in which all infinite products exist and the functors of infinite product are exact. A complex C• over A is called Italic if it belongs to the minimal triangulated subcategory Acycl ctr (A) of the homotopy category Hot(A) containing all the total complexes of exact triples ′K• → K• → ″K• of complexes over A and closed under ...
Leonid Positselski, Sergey Arkhipov, Dmitriy Rumynin   +2 more
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Derived Functors

2023
Simon Lentner, Svea Nora Mierach, Christoph Schweigert, Yorck Sommerhäuser   +3 more
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Relative left derived functors of tensor product functors

Acta Mathematica Sinica, English Series, 2016
The aim of the paper is to introduce and study the relative left derived functor \(\mathrm{Tor}_n^{(\mathcal{F}, \mathcal{F'})} (-,-)\) induced by the tensor product. Let \((\mathcal{C}, \mathcal{D})\) be a balanced pair in Mod-\(R\), let \((\mathcal{C'}, \mathcal{D'})\) be a balanced pair in \(R\)-Mod, let \(\mathcal{F}\) be a precovering subcategory ...
Wang, Jun Fu, Huang, Zhao Yong
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Derived Functors of Graded Theories

K-Theory, 1999
This paper introduces the concept of graded theories. The motivating example is the homotopy category of finite one-point unions of spheres of dimension at least two. In general, a graded theory is a category \({\mathcal T}\) with a set of generating objects \({\mathcal S}\) such that the objects of \({\mathcal T}\) are the finite sums of the members ...
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Derived Functors and Sheaf Cohomology

2019
The aim of the book is to present a precise and comprehensive introduction to the basic theory of derived functors, with an emphasis on sheaf cohomology and spectral sequences. It keeps the treatment as simple as possible, aiming at the same time to provide a number of examples, mainly from sheaf theory, and also from algebra.
Bruzzo, Ugo, Graña Otero, Beatriz
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Derived Categories and Derived Functors

1996
Homological algebra was founded by D. Hilbert. He considered, in particular, the following problem. Let Σ j=1 m a ij x j = 0, i =1,..., n, a ij ∈ k[t 1,..., t r ], be a system of linear homogeneous equations with coefficients lying in the polynomial ring over a field.
Sergei I. Gelfand, Yuri I. Manin
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Jacobi–Trudi Identity and Drinfeld Functor for Super Yangian

International Mathematics Research Notices, 2021
Kang Lu, Evgeny Mukhin
exaly