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18 relations: Category (mathematics), Chain complex, Coherent sheaf, Derivator, Derived category, Differential algebra, Differential graded algebra, Graded (mathematics), Graded category, Grothendieck category, Homological algebra, Mathematics, Model category, Proper morphism, Scheme (mathematics), Smooth morphism, Spectrum (topology), Triangulated category.
Category (mathematics)
In mathematics, a category (sometimes called an abstract category to distinguish it from a concrete category) is an algebraic structure similar to a group but without requiring inverse or closure properties.
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Chain complex
In mathematics, a chain complex is an algebraic structure that consists of a sequence of abelian groups (or modules) and a sequence of homomorphisms between consecutive groups such that the image of each homomorphism is included in the kernel of the next.
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Coherent sheaf
In mathematics, especially in algebraic geometry and the theory of complex manifolds, coherent sheaves are a class of sheaves closely linked to the geometric properties of the underlying space.
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Derivator
In mathematics, derivators are a proposed new framework for homological algebra and various generalisations.
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Derived category
In mathematics, the derived category D(A) of an abelian category A is a construction of homological algebra introduced to refine and in a certain sense to simplify the theory of derived functors defined on A. The construction proceeds on the basis that the objects of D(A) should be chain complexes in A, with two such chain complexes considered isomorphic when there is a chain map that induces an isomorphism on the level of homology of the chain complexes.
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Differential algebra
In mathematics, differential rings, differential fields, and differential algebras are rings, fields, and algebras equipped with finitely many derivations, which are unary functions that are linear and satisfy the Leibniz product rule.
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Differential graded algebra
In mathematics, in particular abstract algebra and topology, a differential graded algebra is a graded algebra with an added chain complex structure that respects the algebra structure.
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Graded (mathematics)
In mathematics, the term “graded” has a number of meanings, mostly related: In abstract algebra, it refers to a family of concepts.
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Graded category
A graded category is a mathematical concept.
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Grothendieck category
In mathematics, a Grothendieck category is a certain kind of abelian category, introduced in Alexander Grothendieck's Tôhoku paper of 1957.
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Homological algebra
Homological algebra is the branch of mathematics that studies homology in a general algebraic setting.
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Mathematics
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
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Model category
In mathematics, particularly in homotopy theory, a model category is a category with distinguished classes of morphisms ('arrows') called 'weak equivalences', 'fibrations' and 'cofibrations'.
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Proper morphism
In algebraic geometry, a proper morphism between schemes is an analog of a proper map between complex analytic spaces.
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Scheme (mathematics)
In mathematics, a scheme is a mathematical structure that enlarges the notion of algebraic variety in several ways, such as taking account of multiplicities (the equations x.
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Smooth morphism
In algebraic geometry, a morphism f:X \to S between schemes is said to be smooth if.
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Spectrum (topology)
In algebraic topology, a branch of mathematics, a spectrum is an object representing a generalized cohomology theory.
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Triangulated category
In mathematics, a triangulated category is a category together with the additional structure of a "translation functor" and a class of "distinguished triangles".
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References
[1] https://en.wikipedia.org/wiki/Differential_graded_category
