coconePointsIsoOfNatIso_hom_desc — Mathlib

English

For F ≅ G, and cocones s,t with IsColimit, the inverse desc equals Q.map w.inv composed with s.ι.app? Actually the statement: (coconePointsIsoOfNatIso P Q w).inv ≫ P.desc r = Q.map r w.inv.

Русский

Для F ≅ G и коконов s,t с IsColimit выполняется: (coconePointsIsoOfNatIso P Q w).inv ≫ P.desc r = Q.map r w.inv.

LaTeX

$$$ (coconePointsIsoOfNatIso P Q w).inv \; ≫ \; P.desc r = Q.map \; r \; w.inv $$$

Lean4

@[reassoc]
theorem coconePointsIsoOfNatIso_hom_desc {F G : J ⥤ C} {s : Cocone F} {r t : Cocone G} (P : IsColimit s)
    (Q : IsColimit t) (w : F ≅ G) : (coconePointsIsoOfNatIso P Q w).hom ≫ Q.desc r = P.map _ w.hom :=
  P.hom_ext (by simp)

Похожие утверждения