associator — Mathlib

English

The symmetry of the braiding yields the inverse property with respect to the product projection maps.

Русский

Симметрия braiding дает обратное свойство относительно проекций произведения.

LaTeX

$$$(prod.braiding P Q).hom ≫ (prod.braiding Q P).hom = id_{P\times Q}$$$

Lean4

/-- The associator isomorphism for binary products. -/
@[simps]
def associator [HasBinaryProducts C] (P Q R : C) : (P ⨯ Q) ⨯ R ≅ P ⨯ Q ⨯ R
    where
  hom := prod.lift (prod.fst ≫ prod.fst) (prod.lift (prod.fst ≫ prod.snd) prod.snd)
  inv := prod.lift (prod.lift prod.fst (prod.snd ≫ prod.fst)) (prod.snd ≫ prod.snd)

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