inj_iso_hom — Mathlib

English

For i with hi: p i = j, the composition X.ιMapObj p i j hi ≫ (c.iso hc).inv equals c.inj ⟨i, hi⟩; this relates the injection to the isomorphism inverse.

Русский

Для i с hi: p i = j, композиция X.ιMapObj p i j hi затем (c.iso hc).inv равна c.inj ⟨i, hi⟩; relates инъекция и инверсия изоморфизма.

LaTeX

$$$ X.ιMapObj p i j hi \;\; ≫ (c.iso hc).inv = c.inj ⟨i, hi⟩ $$$

Lean4

@[reassoc (attr := simp)]
theorem inj_iso_hom (i : I) (hi : p i = j) : c.inj ⟨i, hi⟩ ≫ (c.iso hc).hom = X.ιMapObj p i j hi := by
  apply IsColimit.comp_coconePointUniqueUpToIso_hom

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