Mathlib Map

Theorems · Theorem · group theory

groupHomology.map_chainsFunctor_shortExact

∀ {k G : Type u} [inst : CommRing k] [inst_1 : Group G] {X : CategoryTheory.ShortComplex (Rep.{u, u, u} k G)},
  X.ShortExact → (X.map (groupHomology.chainsFunctor k G)).ShortExact
Defined in
Mathlib.RepresentationTheory.Homological.GroupHomology.LongExactSequence
Cited by
8 results in Mathlib
Foundations
Depth 121 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.δ · cited by 7groupHomology.δgroupHomology.δ_apply · cited by 2groupHomology.δ_applygroupHomology.mapShortComplex₁ · cited by 1groupHomology.mapShortCom…groupHomology.mapShortComplex₃ · cited by 1groupHomology.mapShortCom…groupHomology.map_chainsFunctor_eval_shortExact · cited by 1groupHomology.map_chainsF…groupHomology.mono_δ_of_isZero · cited by 0groupHomology.mono_δ_of_i…groupHomology.epi_δ_of_isZero · cited by 0groupHomology.epi_δ_of_is…groupHomology.isIso_δ_of_isZero · cited by 0groupHomology.isIso_δ_of_…groupHomology.mapShortComplex₁_exact · cited by 0groupHomology.mapShortCom…groupHomology.mapShortComplex₂_exact · cited by 0groupHomology.mapShortCom…groupHomology.mapShortComplex₃_exact · cited by 0groupHomology.mapShortCom…CommRing · cited by 17173CommRingGroup · cited by 6238GroupCategoryTheory.ShortComplex · cited by 1850CategoryTheory.ShortCompl…ModuleCat · cited by 1429ModuleCatLinearMap.range · cited by 893LinearMap.rangeLinearMap.ker · cited by 848LinearMap.kerRep · cited by 843RepCategoryTheory.ShortComplex.g · cited by 658ShortComplex.gCategoryTheory.ShortComplex.f · cited by 653ShortComplex.fComplexShape.down · cited by 605ComplexShape.downChainComplex · cited by 350ChainComplexModuleCat.Hom.hom · cited by 341Hom.homCategoryTheory.forget₂ · cited by 260CategoryTheory.forget₂CategoryTheory.ShortComplex.ShortExact · cited by 232ShortComplex.ShortExactRepresentation.IntertwiningMap.toLinearMap · cited by 205IntertwiningMap.toLinearM…groupHomology.map_chainsFunct…CITED BYCITES

Cites32

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by11

Results whose statement or proof uses this declaration.