isoOfMkEqMk — Mathlib

English

If there is a commutative triangle i1, i2 with a connecting f, then Subobject mk i1 is strictly less than Subobject mk i2 when f is not an isomorphism.

Русский

Если существует коммутативный треугольник с f не изоморфизмом, то mk i1 < mk i2.

LaTeX

$$$\text{Subobject.mk } i_1 < \text{Subobject.mk } i_2$ under the hypotheses$$

Lean4

/-- An equality of subobjects gives an isomorphism of the corresponding objects. -/
@[simps]
def isoOfMkEqMk {B A₁ A₂ : C} (f : A₁ ⟶ B) (g : A₂ ⟶ B) [Mono f] [Mono g] (h : mk f = mk g) : A₁ ≅ A₂
    where
  hom := ofMkLEMk f g h.le
  inv := ofMkLEMk g f h.ge

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