one_braiding — Mathlib

English

The unit η is preserved by braiding with the unit object: η ≫ β_{X,Y}^hom = η.

Русский

Единица η сохраняется при braiding с единичным объектом: η ≫ β_{X,Y}^hom = η.

LaTeX

$$$\\eta \\; ≫ \\; (β_{X,Y})^{\\mathrm{hom}} = η$$$

Lean4

theorem one_braiding (X Y : C) [MonObj X] [MonObj Y] : η ≫ (β_ X Y).hom = η :=
  by
  simp only [tensorObj.one_def, Category.assoc, BraidedCategory.braiding_naturality, braiding_tensorUnit_right,
    Iso.cancel_iso_inv_left]
  monoidal

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