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Derived Categories and Derived Functors
1996Homological 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.
Yuri I. Manin, Sergei Gelfand
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Derived categories and functors [PDF]
, 1971 For each abelian category A, there is a category D(A), called the derived category of A, whose objects are complexes of objects of A, and whose morphisms are formal fractions of homotopy classes of complex morphisms having as denominators homotopy classes inducing isomorphisms in cohomology. If F : A →B is an additive functor between abelian categories,
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ON THE DERIVED CATEGORY AND K-FUNCTOR OF COHERENT SHEAVES ON INTERSECTIONS OF QUADRICS
, 1989A graded Clifford algebra connected with the complete intersection of several quadrics is considered. In terms of modules over this algebra, a description is given of the derived category of coherent sheaves and the Quillen K-functor of the intersection ...
M. Kapranov
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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).
Dmitriy Rumynin +2 more
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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).
Dmitriy Rumynin +2 more
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Derived Categories and Derived Functors
2018This is an introduction to the language of derived categories and understanding the triangulated structure on the derived category. We also introduce the analogue of functors on a derived category, i.e. derived functors.
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2000
In contrast to Cech cohomology groups, which have a long history of successful applications in algebraic topology, Cech homology groups did not prove very useful. This is because the Cech cohomology groups satisfy the exactness axiom, while the Cech homology groups do not.
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In contrast to Cech cohomology groups, which have a long history of successful applications in algebraic topology, Cech homology groups did not prove very useful. This is because the Cech cohomology groups satisfy the exactness axiom, while the Cech homology groups do not.
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On functors with given derivatives
Journal of Soviet Mathematics, 1993This paper considers searching for a functor whose left and right derivative functors are given. Sufficient conditions are provided for solvability of the problem.
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Derived Functors and Sheaf Cohomology
2019The 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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Stable base changeℂ/ℝ of certain derived functor modules
, 1990Joseph F. Johnson
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