Theorems · Definition · algebraic topology

HomotopyGroup.homotopyGroupOfUniqueMulEquivFundamentalGroup

{X : Type u_2} →
  [inst : TopologicalSpace X] →
    {x : X} → (N : Type u_3) → [inst_1 : Unique N] → HomotopyGroup N X x ≃* FundamentalGroup X x

The homotopy group at x indexed by a singleton is isomorphic to the fundamental group, i.e. the loops based at x up to homotopy.

Defined in

Mathlib.Topology.Homotopy.HomotopyGroup

Cited by

0 results in Mathlib

Foundations

Depth 171 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceUnique