Theorems · Definition · group theory
groupHomology.shortComplexH1
{k G : Type u} →
[inst : CommRing k] → [inst_1 : Group G] → Rep.{u, u, u} k G → CategoryTheory.ShortComplex (ModuleCat k)The short complex (G² →₀ A) --d₂₁--> (G →₀ A) --d₁₀--> A.
- Cited by
- 37 results in Mathlib
- Foundations
- Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- CategoryTheory.ShortComplexstatement · cited by 1,850
- ModuleCatstatement · cited by 1,429
- Repstatement and proof · cited by 843
- groupHomology.d₁₀proof · cited by 29
- groupHomology.d₂₁proof · cited by 27
- groupHomology.d₂₁_comp_d₁₀proof · cited by 4
Cited by43
Results whose statement or proof uses this declaration.
- groupHomology.mapCycles₁proof · cited by 20
- groupHomology.isoCycles₁proof · cited by 19
- groupHomology.mapShortComplexH1statement · cited by 14
- groupHomology.H1Isostatement and proof · cited by 7
- groupHomology.isoCycles₁_hom_comp_istatement and proof · cited by 5
- groupHomology.mapShortComplexH1_τ₂statement · cited by 5
- groupHomology.H1π_eq_zero_iffproof · cited by 4
- groupHomology.π_comp_H1Iso_homstatement and proof · cited by 3
- groupHomology.isoShortComplexH1statement · cited by 3
- groupHomology.mapCycles₁_compproof · cited by 3
- groupHomology.mapShortComplexH1_τ₁statement · cited by 3
- groupHomology.H1ToTensorOfIsTrivialproof · cited by 3