Theorems · Inductive type · category theory
CategoryTheory.Localization.HasSmallLocalizedHom
{C : Type u₁} → [inst : CategoryTheory.Category.{v₁, u₁} C] → CategoryTheory.MorphismProperty C → C → C → PropThis property holds if the type of morphisms between X and Y
in the localized category with respect to W : MorphismProperty C
is small.
- Cited by
- 30 results in Mathlib
- Foundations
- Depth 3 from the axioms · uses no axioms
- Assumes
- CategoryTheory.Category
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.MorphismPropertystatement · cited by 2,179
Cited by44
Results whose statement or proof uses this declaration.
- CategoryTheory.Localization.HasSmallLocalizedShiftedHomproof · cited by 41
- CategoryTheory.ShortComplex.ShortExact.extClassproof · cited by 36
- CategoryTheory.Localization.SmallHom.equivstatement and proof · cited by 25
- CategoryTheory.Localization.SmallHomstatement and proof · cited by 24
- CategoryTheory.Localization.SmallHom.mkstatement and proof · cited by 12
- CategoryTheory.Localization.SmallHom.compstatement and proof · cited by 11
- CategoryTheory.Localization.SmallHom.equiv_compstatement and proof · cited by 11
- CategoryTheory.Localization.SmallHom.equiv_mkstatement and proof · cited by 11
- CategoryTheory.Localization.hasSmallLocalizedHom_iffstatement and proof · cited by 6
- CategoryTheory.Localization.SmallHom.mkInvstatement and proof · cited by 5
- CategoryTheory.LocalizerMorphism.smallHomMapstatement and proof · cited by 5
- CategoryTheory.LocalizerMorphism.smallShiftedHomMapproof · cited by 5