Theorems · Theorem · category theory

CategoryTheory.Localization.hasSmallLocalizedHom_iff_of_isos

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] (W : CategoryTheory.MorphismProperty C) {X Y X' Y' : C}
  (e : X ≅ X') (e' : Y ≅ Y'),
  CategoryTheory.Localization.HasSmallLocalizedHom W X Y ↔ CategoryTheory.Localization.HasSmallLocalizedHom W X' Y'

Defined in: Mathlib.CategoryTheory.Localization.SmallHom
Cited by: 2 results in Mathlib
Foundations: Depth 89 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category

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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
CategoryTheory.Isostatement and proof · cited by 3,963
CategoryTheory.MorphismPropertystatement and proof · cited by 2,179
CategoryTheory.Functor.mapIsoproof · cited by 224
CategoryTheory.MorphismProperty.Qproof · cited by 98
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 by2

Results whose statement or proof uses this declaration.

CategoryTheory.Localization.hasSmallLocalizedHom_of_isosproof · cited by 2
CategoryTheory.Localization.hasSmallLocalizedHom_of_hasSmallLocalizedShiftedHom₀proof · cited by 1