Theorems · Theorem · category theory
CategoryTheory.MorphismProperty.isLocallyPresentable_isLocal
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] (W : CategoryTheory.MorphismProperty C) (κ : Cardinal.{w})
[inst_1 : Fact κ.IsRegular] [CategoryTheory.IsCardinalLocallyPresentable C κ]
[CategoryTheory.MorphismProperty.IsSmall.{w, v, u} W],
(∀ ⦃X Y : C⦄ (f : X ⟶ Y), W f → CategoryTheory.IsCardinalPresentable X κ ∧ CategoryTheory.IsCardinalPresentable Y κ) →
CategoryTheory.IsCardinalLocallyPresentable W.isLocal.FullSubcategory κ- Cited by
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- Foundations
- Depth 110 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites18
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
- Factstatement and proof · cited by 2,726
- Cardinalstatement and proof · cited by 2,598
- CategoryTheory.MorphismPropertystatement and proof · cited by 2,179
- CategoryTheory.ObjectProperty.FullSubcategorystatement · cited by 726
- Cardinal.IsRegularstatement and proof · cited by 282
- CategoryTheory.ObjectProperty.ιproof · cited by 95
- CategoryTheory.Functor.IsRightAdjointproof · cited by 46
- CategoryTheory.IsCardinalPresentablestatement and proof · cited by 39
- CategoryTheory.MorphismProperty.isLocalstatement and proof · cited by 22
- CategoryTheory.Functor.IsCardinalAccessibleproof · cited by 19
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