ι_descMapObj — Mathlib

English

For i ∈ I with hi: p i = j, the injection c.inj ⟨i, hi⟩ followed by the isomorphism (c.iso hc).hom equals the injection X.ιMapObj p i j hi.

Русский

Для i ∈ I с hi: p i = j, инъекция c.inj ⟨i, hi⟩ последована гомоморфизмом из изоморфизма (c.iso hc).hom равна инъекции X.ιMapObj p i j hi.

LaTeX

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

Lean4

@[reassoc (attr := simp)]
theorem ι_descMapObj {A : C} {j : J} (φ : ∀ (i : I) (_ : p i = j), X i ⟶ A) (i : I) (hi : p i = j) :
    X.ιMapObj p i j hi ≫ X.descMapObj p φ = φ i hi := by apply Cofan.IsColimit.fac

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