Concept information
Preferred term
derived category
Definition(s)
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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. Derived functors can then be defined for chain complexes, refining the concept of hypercohomology. The definitions lead to a significant simplification of formulas otherwise described (not completely faithfully) by complicated spectral sequences.
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Derived_category)
Broader concept(s)
In other languages
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French
URI
http://data.loterre.fr/ark:/67375/PSR-G03FKLMF-T
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