objEquiv — Mathlib

English

Opposite of LeftFractionRel yields RightFractionRel: if z1,z2 are left-related, then z1.op,z2.op are right-related.

Русский

Противоположность LeftFractionRel даёт RightFractionRel: если z1,z2 связаны левым отношением, то z1.op,z2.op связаны правым.

LaTeX

$$$LeftFractionRel(z_1,z_2) \Rightarrow RightFractionRel(z_1^{op}, z_2^{op})$$$

Lean4

/-- The canonical bijection between objects in a category and its
localization with respect to a morphism_property `W` -/
@[simps]
def objEquiv : C ≃ W.Localization where
  toFun := W.Q.obj
  invFun X := X.as.obj
  right_inv := by
    rintro ⟨⟨X⟩⟩
    rfl

Похожие утверждения