Theorems · Definition · category theory
CategoryTheory.equivSmallModel
(C : Type u) →
[inst : CategoryTheory.Category.{v, u} C] →
[inst_1 : CategoryTheory.EssentiallySmall.{w, v, u} C] → C ≌ CategoryTheory.SmallModel.{w, v, u} CThe (noncomputable) categorical equivalence between an essentially small category and its small model.
- Defined in
- Mathlib.CategoryTheory.EssentiallySmall
- Cited by
- 20 results in Mathlib
- Foundations
- Depth 11 from the axioms · uses Classical.choice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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.Equivalencestatement · cited by 601
- Nonempty.someproof · cited by 340
- CategoryTheory.EssentiallySmallstatement and proof · cited by 42
- CategoryTheory.SmallModelstatement · cited by 15
Cited by31
Results whose statement or proof uses this declaration.
- CategoryTheory.finallySmall_of_essentiallySmallproof · cited by 2
- CategoryTheory.IsCardinalFilteredGenerator.of_isDenseproof · cited by 1
- CategoryTheory.hasSheafifyEssentiallySmallSitestatement and proof · cited by 1
- CategoryTheory.IsFiltered.SmallFilteredIntermediate.factoringproof · cited by 1
- CategoryTheory.IsFiltered.SmallFilteredIntermediate.inclusionproof · cited by 1
- CategoryTheory.FinallySmall.exists_of_isFilteredproof · cited by 1
- CategoryTheory.ObjectProperty.of_essentiallySmall_indexproof · cited by 1
- CategoryTheory.OrthogonalReflection.D₂.hasColimitsOfShapeproof · cited by 1