Theorems · Definition · group theory
groupCohomology.H1
{k G : Type u} → [inst : CommRing k] → [inst_1 : Group G] → Rep.{u, u, u} k G → ModuleCat kShorthand for the 1st group cohomology of a k-linear G-representation A, H¹(G, A),
defined as the 1st cohomology of the complex of inhomogeneous cochains of A.
- Cited by
- 18 results in Mathlib
- Foundations
- Depth 115 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Groupstatement and proof · cited by 6,238
- ModuleCatstatement · cited by 1,429
- Repstatement and proof · cited by 843
- groupCohomologyproof · cited by 60
Cited by21
Results whose statement or proof uses this declaration.
- groupCohomology.H1πstatement · cited by 15
- groupCohomology.H1IsoOfIsTrivialstatement · cited by 6
- groupCohomology.H1Isostatement · cited by 3
- groupCohomology.H1π_comp_mapstatement · cited by 3
- groupCohomology.H1π_comp_H1IsoOfIsTrivial_homstatement · cited by 2
- groupCohomology.H1π_eq_zero_iffstatement and proof · cited by 2
- groupCohomology.π_comp_H1Iso_homstatement · cited by 2
- groupCohomology.H1_induction_onstatement and proof · cited by 1
- groupCohomology.H1π_comp_H1IsoOfIsTrivial_hom_applystatement · cited by 1
- groupCohomology.H1π_comp_map_applystatement · cited by 1
- groupCohomology.H1π_eq_iffstatement and proof · cited by 1
- groupCohomology.H1IsoOfIsTrivial_H1π_apply_applystatement · cited by 0