Theorems · Theorem · category theory
CategoryTheory.Localization.small_of_hasSmallLocalizedHom
∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] (W : CategoryTheory.MorphismProperty C) {D : Type u₂}
[inst_1 : CategoryTheory.Category.{v₂, u₂} D] (L : CategoryTheory.Functor C D) [L.IsLocalization W] (X Y : C)
[CategoryTheory.Localization.HasSmallLocalizedHom W X Y], Small.{w, v₂} (L.obj X ⟶ L.obj Y)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 89 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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 · cited by 32,603
- CategoryTheory.Functor.objstatement · cited by 19,642
- CategoryTheory.Functorstatement and proof · cited by 16,252
- CategoryTheory.MorphismPropertystatement and proof · cited by 2,179
- CategoryTheory.Functor.IsLocalizationstatement and proof · cited by 432
- Smallstatement · cited by 369
- CategoryTheory.Localization.HasSmallLocalizedHomstatement and proof · cited by 30
- CategoryTheory.Localization.hasSmallLocalizedHom_iffproof · cited by 6
Cited by1
Results whose statement or proof uses this declaration.
- CategoryTheory.Localization.SmallHom.equiv_compproof · cited by 11