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gptkbp:instanceOf
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gptkb:mathematical_concept
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gptkbp:category
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gptkb:Bounded_derived_category
gptkb:Unbounded_derived_category
Bounded above derived category
Bounded below derived category
Chain complexes
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gptkbp:citation
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gptkb:Jean-Louis_Verdier's_thesis
Gelfand & Manin, 'Methods of Homological Algebra'
SGA 4 1/2
Weibel, 'An Introduction to Homological Algebra'
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gptkbp:defines
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Category obtained from the category of chain complexes by formally inverting quasi-isomorphisms
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gptkbp:enables
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gptkb:Spectral_sequences
Derived functors
Ext and Tor functors
Homological methods in algebraic geometry
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gptkbp:field
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gptkb:Algebraic_geometry
Homological algebra
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gptkbp:generalizes
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gptkb:Homotopy_category
Abelian category
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https://www.w3.org/2000/01/rdf-schema#label
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Derived category
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gptkbp:importantFor
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gptkb:D-branes_in_string_theory
gptkb:Fourier–Mukai_transform
gptkb:Grothendieck_duality
gptkb:Mirror_symmetry
gptkb:Perverse_sheaves
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gptkbp:introduced
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gptkb:Jean-Louis_Verdier
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gptkbp:introducedIn
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1960s
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gptkbp:morphisms
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Roof diagrams
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gptkbp:notation
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D(A)
D^+(A)
D^-(A)
D^b(A)
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gptkbp:objects
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Chain complexes modulo quasi-isomorphism
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gptkbp:relatedTo
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gptkb:Cohomology
Complex of objects
Sheaf
Triangulated category
t-structure
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gptkbp:usedIn
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gptkb:Algebraic_topology
gptkb:Algebraic_geometry
gptkb:Representation_theory
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gptkbp:bfsParent
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gptkb:algebraic_geometry
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gptkbp:bfsLayer
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5
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