Theorems · Theorem · category theory
CategoryTheory.MorphismProperty.relative_map_iff
∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
{F : CategoryTheory.Functor C D} {P : CategoryTheory.MorphismProperty C} [F.Faithful] [F.Full]
[CategoryTheory.Limits.PreservesLimitsOfShape CategoryTheory.Limits.WalkingCospan F]
[CategoryTheory.Limits.HasPullbacks C] [P.IsStableUnderBaseChange] {X Y : C} {f : X ⟶ Y},
CategoryTheory.MorphismProperty.relative F P (F.map f) ↔ P f- Cited by
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- Foundations
- Depth 39 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement and proof · cited by 32,673
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.Functor.objstatement and proof · cited by 19,642
- CategoryTheory.Functorstatement and proof · cited by 16,252
- CategoryTheory.Functor.mapstatement and proof · cited by 8,698
- CategoryTheory.MorphismPropertystatement and proof · cited by 2,179
- CategoryTheory.Limits.WalkingPairstatement · cited by 1,319
- CategoryTheory.Limits.WalkingCospanstatement and proof · cited by 496
- CategoryTheory.Limits.HasPullbacksstatement and proof · cited by 439
- CategoryTheory.Functor.Fullstatement and proof · cited by 341
- CategoryTheory.Functor.Faithfulstatement and proof · cited by 313
- CategoryTheory.Limits.PreservesLimitsOfShapestatement and proof · cited by 156
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