Commit 2025-07-02 03:33 fcbb8034
View on Github →feat(RepresentationTheory/GroupCohomology): long exact sequences (#25872)
Given a commutative ring k
and a group G
, this PR shows that a short exact sequence of k
-linear G
-representations
0 ⟶ X₁ ⟶ X₂ ⟶ X₃ ⟶ 0
induces a short exact sequence of complexes
0 ⟶ inhomogeneousCochains X₁ ⟶ inhomogeneousCochains X₂ ⟶ inhomogeneousCochains X₃ ⟶ 0
.
Since the cohomology of inhomogeneousCochains Xᵢ
is the group cohomology of Xᵢ
, this allows us to specialize API about long exact sequences to group cohomology.