|
gptkbp:instanceOf
|
gptkb:Functor
|
|
gptkbp:appearsIn
|
spectral sequence
long exact sequence
|
|
gptkbp:category
|
abelian category
|
|
gptkbp:computes
|
extensions of modules
|
|
gptkbp:degree
|
n (non-negative integer)
|
|
gptkbp:Ext^0(A,B)
|
Hom(A,B)
|
|
gptkbp:Ext^1(A,B)
|
equivalence classes of extensions of A by B
|
|
gptkbp:field
|
homological algebra
|
|
gptkbp:firstAppearance
|
1950s
|
|
gptkbp:functorialIn
|
both arguments
|
|
gptkbp:generalizes
|
extension group
group cohomology
sheaf cohomology
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
Ext functor
|
|
gptkbp:input
|
two modules
|
|
gptkbp:introduced
|
gptkb:Henri_Cartan
gptkb:Samuel_Eilenberg
|
|
gptkbp:notation
|
Ext^n(A,B)
|
|
gptkbp:originatedIn
|
right derived functor of Hom
|
|
gptkbp:output
|
abelian group
|
|
gptkbp:relatedTo
|
gptkb:Tor_functor
derived functor
|
|
gptkbp:usedFor
|
classifying module extensions
cohomology theories
measuring non-exactness of Hom
|
|
gptkbp:usedIn
|
gptkb:algebra
gptkb:algebraic_geometry
gptkb:topology
gptkb:category_theory
representation theory
|
|
gptkbp:bfsParent
|
gptkb:commutative_algebra
|
|
gptkbp:bfsLayer
|
5
|