auxGroup — Mathlib

English

The auxiliary groups for different coordinates i and j coincide as groups on the homotopy quotient.

Русский

Группы-ассистенты по разным координатам i и j совпадают как группы на factoring of Homotopy.

LaTeX

$$$(\\mathrm{auxGroup}\\ i) = (\\mathrm{auxGroup}\n j)$ as groups$$

Lean4

/-- Group structure on `HomotopyGroup` obtained by pulling back path composition along the
  `i`th direction. The group structures for two different `i j : N` distribute over each
  other, and therefore are equal by the Eckmann-Hilton argument. -/
abbrev auxGroup (i : N) : Group (HomotopyGroup N X x) :=
  (homotopyGroupEquivFundamentalGroup i).group

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