Theorems · Theorem · algebraic topology

IsQuotientCoveringMap.fundamentalGroupToMulOpposite_apply_eq_Iff

∀ {E : Type u_1} {X : Type u_2} [inst : TopologicalSpace E] [inst_1 : TopologicalSpace X] {p : E → X} {G : Type u_4}
  [inst_2 : Group G] [inst_3 : MulAction G E] (hp : IsQuotientCoveringMap p G) {x : X} {e : ↑(p ⁻¹' {x})}
  {γ : FundamentalGroup X x} {g : Gᵐᵒᵖ},
  (hp.fundamentalGroupToMulOpposite e) γ = g ↔ MulOpposite.unop g • ↑e = ↑(⋯.monodromy γ e)

Defined in

Mathlib.Topology.Homotopy.Lifting

Cited by

2 results in Mathlib

Foundations

Depth 143 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpaceGroupMulAction