Theorems · Theorem · category theory

CategoryTheory.ObjectProperty.exists_equivalence_iff

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] (P : CategoryTheory.ObjectProperty C)
  [CategoryTheory.LocallySmall.{w', v, u} C],
  (∃ J x, Nonempty (P.FullSubcategory ≌ J)) ↔ CategoryTheory.ObjectProperty.EssentiallySmall.{w, v, u} P

Defined in: Mathlib.CategoryTheory.ObjectProperty.Small
Cited by: 1 results in Mathlib
Foundations: Depth 31 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.LocallySmall

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Cites26

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.Functor.objproof · cited by 19,642
CategoryTheory.Functor.compproof · cited by 6,529
CategoryTheory.Equivalence.functorproof · cited by 1,268
CategoryTheory.Equivalence.inverseproof · cited by 1,130
CategoryTheory.ObjectPropertystatement and proof · cited by 798
CategoryTheory.ObjectProperty.FullSubcategorystatement and proof · cited by 726
CategoryTheory.Equivalencestatement and proof · cited by 601
CategoryTheory.Equivalence.unitIsoproof · cited by 536
CategoryTheory.Iso.appproof · cited by 253
CategoryTheory.LocallySmallstatement and proof · cited by 242
CategoryTheory.Functor.mapIsoproof · cited by 224

Cited by1

Results whose statement or proof uses this declaration.

CategoryTheory.exists_equivalence_iff_of_locallySmallproof · cited by 2