coflat_of_preservesFiniteColimits

English

Representably Coflat functors preserve finite colimits; equivalently, coflatness corresponds to preservation of finite colimits under opposites.

Русский

Representably cof flat функторы сохраняют конечные колимиты; эквивалентно сохранению конечных колимитов при противоположностях.

LaTeX

$$$\text{RepresentablyCoflat } F \Rightarrow \text{PreservesFiniteColimits } F$$$

Lean4

theorem coflat_of_preservesFiniteColimits [HasFiniteColimits C] (F : C ⥤ D) [PreservesFiniteColimits F] :
    RepresentablyCoflat F :=
  let _ := preservesFiniteLimits_op F
  (representablyFlat_op_iff _).1 (flat_of_preservesFiniteLimits _)

Похожие утверждения