Statements (28)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:appearsIn |
Long exact sequence in homology
|
| gptkbp:category |
gptkb:Functor
Derived functor |
| gptkbp:computes |
Flat resolution
Projective resolution |
| gptkbp:defines |
Derived functor of the tensor product
|
| gptkbp:degreeZero |
Tor_0^R(A,B) = A ⊗_R B
|
| gptkbp:field |
gptkb:algebra
Homological algebra |
| gptkbp:generalizes |
gptkb:Tensor_product
|
| gptkbp:higherDegrees |
Measures failure of flatness
|
| https://www.w3.org/2000/01/rdf-schema#label |
Tor functor
|
| gptkbp:introduced |
gptkb:Henri_Cartan
gptkb:Samuel_Eilenberg |
| gptkbp:notation |
Tor_n^R(A,B)
|
| gptkbp:output |
Abelian group
|
| gptkbp:property |
Additive functor
Right exact |
| gptkbp:relatedTo |
gptkb:Ext_functor
gptkb:Tensor_product |
| gptkbp:requires |
gptkb:King
Module |
| gptkbp:usedIn |
gptkb:Algebraic_topology
gptkb:Algebraic_geometry gptkb:Commutative_algebra |
| gptkbp:bfsParent |
gptkb:commutative_algebra
|
| gptkbp:bfsLayer |
5
|