Theorems · Inductive type · category theory
CategoryTheory.RepresentablyFlat
{C : Type u₁} →
[inst : CategoryTheory.Category.{v₁, u₁} C] →
{D : Type u₂} → [inst_1 : CategoryTheory.Category.{v₂, u₂} D] → CategoryTheory.Functor C D → PropA functor F : C ⥤ D is representably flat if the comma category (X/F) is cofiltered for
each X : D.
- Defined in
- Mathlib.CategoryTheory.Functor.Flat
- Cited by
- 18 results in Mathlib
- Foundations
- Depth 2 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement · cited by 32,673
- CategoryTheory.Functorstatement · cited by 16,252
Cited by24
Results whose statement or proof uses this declaration.
- CategoryTheory.flat_of_preservesFiniteLimitsstatement · cited by 4
- CategoryTheory.compatiblePreservingOfFlatstatement and proof · cited by 3
- CategoryTheory.GrothendieckTopology.Point.comapstatement and proof · cited by 3
- CategoryTheory.PreservesFiniteLimitsOfFlat.liftstatement and proof · cited by 2
- CategoryTheory.GrothendieckTopology.Point.sheafFiberComapIsostatement and proof · cited by 2
- CategoryTheory.preservesFiniteLimits_of_flatstatement and proof · cited by 2
- CategoryTheory.GrothendieckTopology.Point.skyscraperSheafFunctorCompSheafPushforwardContinuousstatement and proof · cited by 2
- CategoryTheory.MorphismProperty.isContinuous_comap_forgetproof · cited by 1
- CategoryTheory.PreservesFiniteLimitsOfFlat.facstatement and proof · cited by 1
- CategoryTheory.PreservesFiniteLimitsOfFlat.uniqstatement and proof · cited by 1
- CategoryTheory.representablyFlat_op_iffstatement and proof · cited by 1
- CategoryTheory.Functor.isContinuous_iff_coverPreservingstatement and proof · cited by 1