Theorems · Definition · group theory
groupHomology.H0
{k G : Type u} → [inst : CommRing k] → [inst_1 : Group G] → Rep.{u, u, u} k G → ModuleCat kShorthand for the 0th group homology of a k-linear G-representation A, H₀(G, A),
defined as the 0th homology of the complex of inhomogeneous chains of A.
- Cited by
- 25 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 by28
Results whose statement or proof uses this declaration.
- groupHomology.H0πstatement · cited by 16
- groupHomology.H0Isostatement · cited by 12
- groupHomology.H0IsoOfIsTrivialstatement · cited by 5
- groupHomology.π_comp_H0Iso_homstatement · cited by 4
- groupHomology.H0π_comp_H0Iso_homstatement · cited by 3
- groupHomology.coinvariantsMk_comp_H0Iso_invstatement · cited by 2
- groupHomology.π_comp_H0IsoOfIsTrivial_homstatement · cited by 2
- groupHomology.map_id_comp_H0Iso_homstatement · cited by 2
- groupHomology.cyclesIso₀_comp_H0πstatement · cited by 2
- groupHomology.H0π_comp_mapstatement · cited by 2
- groupHomology.cyclesIso₀_comp_H0π_applystatement · cited by 1
- groupHomology.H0π_comp_H0Iso_hom_assocstatement · cited by 1