createsColimitOfComp — Mathlib

Lean4

/-- If `F` is final and `F ⋙ G` creates colimits of `H`, then so does `G`. -/
def createsColimitOfComp {B : Type u₄} [Category.{v₄} B] {H : E ⥤ B} [CreatesColimit (F ⋙ G) H] : CreatesColimit G H
    where
  reflects := (reflectsColimit_of_comp F).reflects
  lifts {c}
    hc := by
    refine ⟨(extendCocone (F := F)).obj (liftColimit ((isColimitWhiskerEquiv F _).symm hc)), ?_⟩
    let i := liftedColimitMapsToOriginal (K := (F ⋙ G)) ((isColimitWhiskerEquiv F _).symm hc)
    refine ?_ ≪≫ ((extendCocone (F := F)).mapIso i) ≪≫ ((coconesEquiv F (G ⋙ H)).counitIso.app _)
    exact Cocones.ext (Iso.refl _)

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