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Theorems · Theorem · algebraic topology

IsAddQuotientCoveringMap.toMultiplicative

∀ {E : Type u_1} {X : Type u_2} [inst : TopologicalSpace E] [inst_1 : TopologicalSpace X] (f : E → X) (G : Type u_4)
  [inst_2 : AddGroup G] [inst_3 : AddAction G E],
  IsAddQuotientCoveringMap f G → IsQuotientCoveringMap f (Multiplicative G)
Defined in
Mathlib.Topology.Covering.Quotient
Cited by
12 results in Mathlib
Foundations
Depth 20 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
TopologicalSpaceTopologicalSpaceAddGroupAddAction

Around this declaration

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

IsAddQuotientCoveringMap.fundamentalGroupToMulOpposite · cited by 6IsAddQuotientCoveringMap.…IsAddQuotientCoveringMap.monodromy_ext_iff · cited by 1IsAddQuotientCoveringMap.…IsAddQuotientCoveringMap.commute_monodromyPerm_toPermFiber · cited by 0IsAddQuotientCoveringMap.…IsAddQuotientCoveringMap.fundamentalGroupEquiv · cited by 0IsAddQuotientCoveringMap.…IsAddQuotientCoveringMap.fundamentalGroupToMulOpposite_apply_eq_Iff · cited by 0IsAddQuotientCoveringMap.…IsAddQuotientCoveringMap.fundamentalGroupToMulOpposite_eq_one_iff · cited by 0IsAddQuotientCoveringMap.…IsAddQuotientCoveringMap.fundamentalGroupToMulOpposite_injective · cited by 0IsAddQuotientCoveringMap.…IsAddQuotientCoveringMap.fundamentalGroupToMulOpposite_surjective · cited by 0IsAddQuotientCoveringMap.…IsAddQuotientCoveringMap.ker_fundamentalGroupToMulOpposite · cited by 0IsAddQuotientCoveringMap.…IsAddQuotientCoveringMap.ker_monodromyPerm · cited by 0IsAddQuotientCoveringMap.…IsAddQuotientCoveringMap.monodromyPerm_injective · cited by 0IsAddQuotientCoveringMap.…IsAddQuotientCoveringMap.monodromy_eq_id_iff · cited by 0IsAddQuotientCoveringMap.…IsAddQuotientCoveringMap.monodromy_toPermFiber · cited by 0IsAddQuotientCoveringMap.…IsAddQuotientCoveringMap.unop_fundamentalGroupToMulOpposite_smul · cited by 0IsAddQuotientCoveringMap.…DFunLike.coe · cited by 62936DFunLike.coeSet · cited by 53352SetTopologicalSpace · cited by 24529TopologicalSpaceSet.image · cited by 5609Set.imagenhds · cited by 5554nhdsAddGroup · cited by 4410AddGroupEquiv.symm · cited by 3681Equiv.symmSet.Nonempty · cited by 2627Set.NonemptyHVAdd.hVAdd · cited by 1820HVAdd.hVAddMultiplicative · cited by 875MultiplicativeAddAction · cited by 820AddActionSet.image_congr · cited by 533Set.image_congrMultiplicative.ofAdd · cited by 237Multiplicative.ofAddTopology.IsQuotientMap · cited by 124Topology.IsQuotientMapAddAction.orbit · cited by 86AddAction.orbitIsAddQuotientCoveringMap.toMu…CITED BYCITES

Cites21

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

Cited by14

Results whose statement or proof uses this declaration.