Mathlib Map

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} C

The (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
Assumes
CategoryTheory.CategoryCategoryTheory.EssentiallySmall

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

CategoryTheory.ObjectProperty.IsStrongGenerator.isDense_colimitsCardinalClosure_ι · cited by 2IsStrongGenerator.isDense…CategoryTheory.finallySmall_of_essentiallySmall · cited by 2CategoryTheory.finallySma…CategoryTheory.IsCardinalFilteredGenerator.of_isDense · cited by 1IsCardinalFilteredGenerat…CategoryTheory.ObjectProperty.IsCardinalFilteredGenerator.essentiallyLarge_top · cited by 1IsCardinalFilteredGenerat…CategoryTheory.hasSheafifyEssentiallySmallSite · cited by 1CategoryTheory.hasSheafif…CategoryTheory.IsFiltered.SmallFilteredIntermediate.factoring · cited by 1SmallFilteredIntermediate…CategoryTheory.IsFiltered.SmallFilteredIntermediate.factoringCompInclusion · cited by 1SmallFilteredIntermediate…CategoryTheory.IsFiltered.SmallFilteredIntermediate.inclusion · cited by 1SmallFilteredIntermediate…CategoryTheory.FinallySmall.exists_of_isFiltered · cited by 1FinallySmall.exists_of_is…CategoryTheory.ObjectProperty.of_essentiallySmall_index · cited by 1ObjectProperty.of_essenti…CategoryTheory.Functor.preservesColimitsOfShape_of_isCardinalAccessible_of_essentiallySmall · cited by 1Functor.preservesColimits…CategoryTheory.OrthogonalReflection.D₂.hasColimitsOfShape · cited by 1D₂.hasColimitsOfShapeCategoryTheory.initiallySmall_of_essentiallySmall · cited by 1CategoryTheory.initiallyS…CategoryTheory.Limits.HasColimitsOfShape.of_essentiallySmall · cited by 0HasColimitsOfShape.of_ess…CategoryTheory.smallSheafificationAdjunction · cited by 0CategoryTheory.smallSheaf…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.Equivalence · cited by 601CategoryTheory.EquivalenceNonempty.some · cited by 340Nonempty.someCategoryTheory.EssentiallySmall · cited by 42CategoryTheory.Essentiall…CategoryTheory.SmallModel · cited by 15CategoryTheory.SmallModelCategoryTheory.equivSmallModelCITED BYCITES

Cites5

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by31

Results whose statement or proof uses this declaration.