CategoryTheory.flat_of_preservesFiniteLimits

theorem CategoryTheory.flat_of_preservesFiniteLimits : ∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} D] [inst_2 : CategoryTheory.Limits.HasFiniteLimits C] (F : CategoryTheory.Functor C D) [inst_3 : CategoryTheory.Limits.PreservesFiniteLimits F], CategoryTheory.RepresentablyFlat F

This theorem states that for any two categories `C` and `D`, where `C` has finite limits, if a functor `F` from `C` to `D` is known to preserve finite limits, then `F` is representably flat. In other words, if a functor takes finite limits in `C` to limits in `D` (preserves finite limits), then it has the property of being representably flat; a functor is representably flat if it reflects certain limit properties of the category structure.

More concisely: If functor `F` from category `C` to category `D` preserves finite limits in `C`, then `F` is representably flat.