Theorems · Definition · algebraic topology

IsCoveringMap.liftPathQuotient

{E : Type u_1} →
  {X : Type u_2} →
    [inst : TopologicalSpace E] →
      [inst_1 : TopologicalSpace X] →
        {p : E → X} →
          (cov : IsCoveringMap p) →
            {x y : X} →
              (γ : Path.Homotopic.Quotient x y) → (e : ↑(p ⁻¹' {x})) → Path.Homotopic.Quotient ↑e ↑(cov.monodromy γ e)

Lift a homotopy class of paths to a covering space.

Defined in

Mathlib.Topology.Homotopy.Lifting

Cited by

3 results in Mathlib

Foundations

Depth 137 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpace