toBiconeIsLimit — Mathlib

English

The colimit property for the binary bicone is equivalent to the colimit property for the original bicone.

Русский

Свойство колимита бинарного бикона эквивалентно свойству колимита исходного бикона.

LaTeX

$$$$ IsColimit(b.toBinaryBicone.toCocone) \simeq IsColimit(b.toCocone) $$$$

Lean4

/-- A binary bicone is a limit cone if and only if the corresponding bicone is a limit cone. -/
def toBiconeIsLimit {X Y : C} (b : BinaryBicone X Y) : IsLimit b.toBicone.toCone ≃ IsLimit b.toCone :=
  IsLimit.equivIsoLimit <| Cones.ext (Iso.refl _) fun ⟨as⟩ => by cases as <;> simp

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