leftAdjointObjIsDefined_of_isColimit

English

Given an IsColimit cocone hc and a family h on j, the left adjoint object is defined on the colimit; specifically, leftAdjointObjIsDefined (colimit R) holds when hc, hc' are IsColimit cocones and h covers each R.obj j.

Русский

При наличии кокона IsColimit hc и семейства h для каждого j, правый левый объект определён на colimit R.

LaTeX

$$$\text{LeftAdjointObjIsDefined}(\text{colimit}\;R)$$$

Lean4

theorem leftAdjointObjIsDefined_of_isColimit {J : Type*} [Category J] {R : J ⥤ C} {c : Cocone R} (hc : IsColimit c)
    [HasColimitsOfShape J D] (h : ∀ (j : J), F.leftAdjointObjIsDefined (R.obj j)) : F.leftAdjointObjIsDefined c.pt :=
  (corepresentableByCompCoyonedaObjOfIsColimit (R := ObjectProperty.lift _ R h) hc
      (colimit.isColimit _)).isCorepresentable

Похожие утверждения