Theorems · Theorem · category theory

CategoryTheory.preservesFiniteColimits_iff_coflat

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
  [CategoryTheory.Limits.HasFiniteColimits C] (F : CategoryTheory.Functor C D),
  CategoryTheory.RepresentablyCoflat F ↔ CategoryTheory.Limits.PreservesFiniteColimits F

If C is finitely cocomplete, then F : C ⥤ D is representably coflat iff it preserves finite colimits.

Defined in: Mathlib.CategoryTheory.Functor.Flat
Cited by: 0 results in Mathlib
Foundations: Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Category CategoryTheory.Limits.HasFiniteColimits

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CategoryTheory.Categorystatement and proof · cited by 32,673
CategoryTheory.Functorstatement and proof · cited by 16,252
CategoryTheory.Limits.PreservesFiniteColimitsstatement and proof · cited by 102
CategoryTheory.Limits.HasFiniteColimitsstatement and proof · cited by 34
CategoryTheory.RepresentablyCoflatstatement and proof · cited by 9
CategoryTheory.preservesFiniteColimits_of_coflatproof · cited by 1
CategoryTheory.coflat_of_preservesFiniteColimitsproof · cited by 1

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