binaryCoproductEquiv — Mathlib

English

The object (F ⨿ G).obj a is in bijection with the disjoint sum F.obj a ⊕ G.obj a, via the hom and its inverse.

Русский

Объект (F ⨿ G).obj a эквивариантно бикратно с F.obj a ⊕ G.obj a через гомограмм и её обратное.

LaTeX

$$$ (F \ ⨿ G).obj a \cong (F.obj a) \oplus (G.obj a) $$$

Lean4

/-- `(F ⨿ G).obj a` is in bijection with disjoint union of `F.obj a` and `G.obj a`. -/
@[simps]
noncomputable def binaryCoproductEquiv (a : C) : (F ⨿ G).obj a ≃ (F.obj a) ⊕ (G.obj a)
    where
  toFun z := (binaryCoproductIso F G).hom.app a z
  invFun z := (binaryCoproductIso F G).inv.app a z
  left_inv _ := by simp only [hom_inv_id_app_apply]
  right_inv _ := by simp only [inv_hom_id_app_apply]

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