Theorems · Definition · algebraic topology

HomotopyGroup.auxGroup

{N : Type u_1} →
  {X : Type u_2} → [inst : TopologicalSpace X] → {x : X} → [DecidableEq N] → N → Group (HomotopyGroup N X x)

Group structure on HomotopyGroup obtained by pulling back path composition along the ith direction. The group structures for two different i j : N distribute over each other, and therefore are equal by the Eckmann-Hilton argument.

Defined in

Mathlib.Topology.Homotopy.HomotopyGroup

Cited by

2 results in Mathlib

Foundations

Depth 164 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceDecidableEq