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Theorems · Theorem · group theory

groupCohomology.map_cochainsFunctor_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 (groupCohomology.cochainsFunctor k G)).ShortExact
Defined in
Mathlib.RepresentationTheory.Homological.GroupCohomology.LongExactSequence
Cited by
9 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.

groupCohomology.δ · cited by 8groupCohomology.δgroupCohomology.δ_apply · cited by 2groupCohomology.δ_applygroupCohomology.mapShortComplex₁ · cited by 1groupCohomology.mapShortC…groupCohomology.mapShortComplex₃ · cited by 1groupCohomology.mapShortC…groupCohomology.map_cochainsFunctor_eval_shortExact · cited by 1groupCohomology.map_cocha…groupCohomology.epi_δ_of_isZero · cited by 0groupCohomology.epi_δ_of_…groupCohomology.mapShortComplex₁_exact · cited by 0groupCohomology.mapShortC…groupCohomology.mapShortComplex₂_exact · cited by 0groupCohomology.mapShortC…groupCohomology.isIso_δ_of_isZero · cited by 0groupCohomology.isIso_δ_o…groupCohomology.mapShortComplex₃_exact · cited by 0groupCohomology.mapShortC…groupCohomology.mono_δ_of_isZero · cited by 0groupCohomology.mono_δ_of…groupCohomology.δ_naturality · cited by 0groupCohomology.δ_natural…CommRing · cited by 17173CommRingGroup · cited by 6238GroupSet.univ · cited by 3945Set.univCategoryTheory.ShortComplex · cited by 1850CategoryTheory.ShortCompl…ModuleCat · cited by 1429ModuleCatComplexShape.up · cited by 1123ComplexShape.upCochainComplex · cited by 1016CochainComplexLinearMap.range · cited by 893LinearMap.rangeLinearMap.ker · cited by 848LinearMap.kerRep · cited by 843RepCategoryTheory.ShortComplex.g · cited by 658ShortComplex.gCategoryTheory.ShortComplex.f · cited by 653ShortComplex.fCategoryTheory.forget₂ · cited by 260CategoryTheory.forget₂CategoryTheory.ShortComplex.ShortExact · cited by 232ShortComplex.ShortExactRepresentation.IntertwiningMap.toLinearMap · cited by 205IntertwiningMap.toLinearM…groupCohomology.map_cochainsF…CITED BYCITES

Cites26

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Cited by12

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