Theorems · Inductive type · category theory
CategoryTheory.EssentiallySmall
(C : Type u) → [CategoryTheory.Category.{v, u} C] → PropA category is EssentiallySmall.{w} if there exists
an equivalence to some S : Type w with [SmallCategory S].
- Defined in
- Mathlib.CategoryTheory.EssentiallySmall
- Cited by
- 42 results in Mathlib
- Foundations
- Depth 1 from the axioms · uses no axioms
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement · cited by 32,673
Cited by52
Results whose statement or proof uses this declaration.
- CategoryTheory.equivSmallModelstatement and proof · cited by 20
- CategoryTheory.SmallModelstatement and proof · cited by 15
- CategoryTheory.IsCardinalPresentable.exists_hom_of_isColimitstatement and proof · cited by 7
- CategoryTheory.preservesColimitsOfShape_of_isCardinalPresentable_of_essentiallySmallstatement and proof · cited by 3
- CategoryTheory.essentiallySmallSelfstatement · cited by 2
- CategoryTheory.essentiallySmall_of_fully_faithfulstatement and proof · cited by 2
- CategoryTheory.IsCardinalPresentable.exists_eq_of_isColimit'statement and proof · cited by 2
- CategoryTheory.finallySmall_of_essentiallySmallstatement and proof · cited by 2
- CategoryTheory.EssentiallySmall.casesOnstatement and proof · cited by 2
- CategoryTheory.EssentiallySmall.mk'statement · cited by 2
- CategoryTheory.MorphismProperty.isClosedUnderColimitsOfShape_isLocalstatement and proof · cited by 1
- CategoryTheory.IsCardinalFilteredGenerator.of_isDensestatement and proof · cited by 1