Theorems · Definition · group theory
groupHomology.H1
{k G : Type u} → [inst : CommRing k] → [inst_1 : Group G] → Rep.{u, u, u} k G → ModuleCat kShorthand for the 1st group homology of a k-linear G-representation A, H₁(G, A),
defined as the 1st homology of the complex of inhomogeneous chains of A.
- Cited by
- 29 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
- groupHomologyproof · cited by 59
Cited by34
Results whose statement or proof uses this declaration.
- groupHomology.H1πstatement · cited by 18
- groupHomology.H1Isostatement · cited by 7
- groupHomology.H1AddEquivOfIsTrivialstatement · cited by 4
- groupHomology.H1π_eq_zero_iffstatement and proof · cited by 4
- groupHomology.π_comp_H1Iso_homstatement · cited by 3
- groupHomology.H1ToTensorOfIsTrivialstatement · cited by 3
- groupHomology.H1π_comp_mapstatement · cited by 3
- groupHomology.mkH1OfIsTrivialstatement · cited by 3
- groupHomology.π_comp_H1Iso_invstatement · cited by 2
- groupHomology.H1_induction_onstatement and proof · cited by 2
- groupHomology.H1π_comp_map_applystatement · cited by 2
- groupHomology.H1π_eq_iffstatement and proof · cited by 2