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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.

Defined in
Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree
Cited by
37 results in Mathlib
Foundations
Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommRingGroup

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

groupHomology.mapCycles₁ · cited by 20groupHomology.mapCycles₁groupHomology.isoCycles₁ · cited by 19groupHomology.isoCycles₁groupHomology.mapShortComplexH1 · cited by 14groupHomology.mapShortCom…groupHomology.H1Iso · cited by 7groupHomology.H1IsogroupHomology.isoCycles₁_hom_comp_i · cited by 5groupHomology.isoCycles₁_…groupHomology.mapShortComplexH1_τ₂ · cited by 5groupHomology.mapShortCom…groupHomology.H1π_eq_zero_iff · cited by 4groupHomology.H1π_eq_zero…groupHomology.π_comp_H1Iso_hom · cited by 3groupHomology.π_comp_H1Is…groupHomology.isoShortComplexH1 · cited by 3groupHomology.isoShortCom…groupHomology.mapCycles₁_comp · cited by 3groupHomology.mapCycles₁_…groupHomology.mapShortComplexH1_τ₁ · cited by 3groupHomology.mapShortCom…groupHomology.H1ToTensorOfIsTrivial · cited by 3groupHomology.H1ToTensorO…groupHomology.toCycles_comp_isoCycles₁_hom · cited by 2groupHomology.toCycles_co…groupHomology.isoCycles₁_inv_comp_iCycles · cited by 2groupHomology.isoCycles₁_…groupHomology.π_comp_H1Iso_inv · cited by 2groupHomology.π_comp_H1Is…CommRing · cited by 17173CommRingGroup · cited by 6238GroupCategoryTheory.ShortComplex · cited by 1850CategoryTheory.ShortCompl…ModuleCat · cited by 1429ModuleCatRep · cited by 843RepgroupHomology.d₁₀ · cited by 29groupHomology.d₁₀groupHomology.d₂₁ · cited by 27groupHomology.d₂₁groupHomology.d₂₁_comp_d₁₀ · cited by 4groupHomology.d₂₁_comp_d₁₀groupHomology.shortComplexH1CITED BYCITES

Cites8

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Cited by43

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