Theorems · Theorem · category theory
CategoryTheory.Localization.hasSmallLocalizedHom_iff_source
∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] (W : CategoryTheory.MorphismProperty C) {X X' : C}
(f : X ⟶ X'),
W f →
∀ (Y : C),
CategoryTheory.Localization.HasSmallLocalizedHom W X Y ↔ CategoryTheory.Localization.HasSmallLocalizedHom W X' Y- Cited by
- 1 results in Mathlib
- Foundations
- Depth 89 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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.objproof · cited by 19,642
- CategoryTheory.MorphismPropertystatement and proof · cited by 2,179
- CategoryTheory.Iso.reflproof · cited by 727
- CategoryTheory.MorphismProperty.Qproof · cited by 98
- CategoryTheory.Localization.isoOfHomproof · cited by 35
- CategoryTheory.Localization.HasSmallLocalizedHomstatement · cited by 30
- CategoryTheory.Iso.homCongrproof · cited by 30
- small_congrproof · cited by 10
- CategoryTheory.Localization.hasSmallLocalizedHom_iffproof · cited by 6
Cited by1
Results whose statement or proof uses this declaration.
- CategoryTheory.Localization.hasSmallLocalizedShiftedHom_iff_sourceproof · cited by 0