Theorems · Definition · general topology

Topology.IsQuotientMap.liftEquiv

{X : Type u_1} →
  {Y : Type u_2} →
    {Z : Type u_3} →
      [inst : TopologicalSpace X] →
        [inst_1 : TopologicalSpace Y] →
          [inst_2 : TopologicalSpace Z] →
            {f : C(X, Y)} → Topology.IsQuotientMap ⇑f → { g // Function.FactorsThrough ⇑g ⇑f } ≃ C(Y, Z)

IsQuotientMap.lift as an equivalence.

Defined in: Mathlib.Topology.ContinuousMap.Basic
Cited by: 3 results in Mathlib
Foundations: Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: TopologicalSpace TopologicalSpace TopologicalSpace

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Cites8

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

DFunLike.coestatement and proof · cited by 62,936
TopologicalSpacestatement and proof · cited by 24,529
Equivstatement · cited by 8,337
ContinuousMapstatement and proof · cited by 2,491
ContinuousMap.compproof · cited by 181
Topology.IsQuotientMapstatement and proof · cited by 124
Function.FactorsThroughstatement and proof · cited by 20
Topology.IsQuotientMap.liftproof · cited by 6

Cited by3

Results whose statement or proof uses this declaration.

Topology.IsQuotientMap.liftEquiv_symm_apply_coestatement and proof · cited by 0
Topology.IsQuotientMap.liftEquiv.congr_simpstatement and proof · cited by 0
Topology.IsQuotientMap.liftEquiv_applystatement and proof · cited by 0