Theorems · Theorem · category theory
CategoryTheory.MorphismProperty.relative_of_snd
∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
{F : CategoryTheory.Functor C D} {X Y : D} {P : CategoryTheory.MorphismProperty C} [F.Faithful] [F.Full]
[P.RespectsIso] {f : X ⟶ Y} (hf : F.relativelyRepresentable f),
(∀ ⦃a : C⦄ (g : F.obj a ⟶ Y), P (hf.snd g)) → CategoryTheory.MorphismProperty.relative F P f- Cited by
- 0 results in Mathlib
- Foundations
- Depth 35 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites15
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.MorphismPropertystatement and proof · cited by 2,179
- CategoryTheory.Functor.Fullstatement and proof · cited by 341
- CategoryTheory.Functor.Faithfulstatement and proof · cited by 313
- CategoryTheory.MorphismProperty.RespectsIsostatement and proof · cited by 248
- CategoryTheory.Functor.relativelyRepresentable.pullbackstatement and proof · cited by 65
- CategoryTheory.Functor.relativelyRepresentablestatement and proof · cited by 64
- CategoryTheory.Functor.relativelyRepresentable.sndstatement and proof · cited by 34
- CategoryTheory.Functor.relativelyRepresentable.fstproof · cited by 16
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