coproducts_le — Mathlib

English

Under appropriate stability assumptions, coproducts P ≤ Q is equivalent to P ≤ Q.

Русский

При подходящих условиях стабильности копродукты P ≤ Q эквивалентны P ≤ Q.

LaTeX

$$coproducts(P) \le Q ↔ P \le Q \text{(при } Q\text{ стабильности})$$

Lean4

theorem coproducts_le [IsStableUnderCoproducts.{w} W] : coproducts.{w} W ≤ W :=
  by
  intro X Y f hf
  rw [coproducts_iff] at hf
  obtain ⟨J, hf⟩ := hf
  exact colimitsOfShape_le _ hf

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