Mathlib Map

Theorems · Definition · category theory

CategoryTheory.SmallModel

(C : Type u) → [inst : CategoryTheory.Category.{v, u} C] → [CategoryTheory.EssentiallySmall.{w, v, u} C] → Type w

An arbitrarily chosen small model for an essentially small category.

Defined in
Mathlib.CategoryTheory.EssentiallySmall
Cited by
15 results in Mathlib
Foundations
Depth 8 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.equivSmallModel · cited by 20CategoryTheory.equivSmall…CategoryTheory.IsCardinalFilteredGenerator.of_isDense · cited by 1IsCardinalFilteredGenerat…CategoryTheory.ObjectProperty.of_essentiallySmall_index · cited by 1ObjectProperty.of_essenti…CategoryTheory.ObjectProperty.IsCardinalFilteredGenerator.essentiallyLarge_top · cited by 1IsCardinalFilteredGenerat…CategoryTheory.hasSheafifyEssentiallySmallSite · cited by 1CategoryTheory.hasSheafif…CategoryTheory.Functor.preservesColimitsOfShape_of_isCardinalAccessible_of_essentiallySmall · cited by 1Functor.preservesColimits…CategoryTheory.FinallySmall.exists_of_isFiltered · cited by 1FinallySmall.exists_of_is…CategoryTheory.IsFiltered.SmallFilteredIntermediate · cited by 1IsFiltered.SmallFilteredI…CategoryTheory.Limits.HasColimitsOfShape.of_essentiallySmall · cited by 0HasColimitsOfShape.of_ess…CategoryTheory.smallSheafificationAdjunction · cited by 0CategoryTheory.smallSheaf…CategoryTheory.smallSheafify · cited by 0CategoryTheory.smallSheaf…CategoryTheory.hasLimitsEssentiallySmallSite · cited by 0CategoryTheory.hasLimitsE…CategoryTheory.Sheaf.isGrothendieckAbelian_of_essentiallySmall · cited by 0Sheaf.isGrothendieckAbeli…LightCondensed.equivSmall · cited by 0LightCondensed.equivSmallLightCondensed.equivSmallFreeIso · cited by 0LightCondensed.equivSmall…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.EssentiallySmall · cited by 42CategoryTheory.Essentiall…CategoryTheory.EssentiallySmall.equiv_smallCategory · cited by 1EssentiallySmall.equiv_sm…CategoryTheory.SmallModelCITED BYCITES

Cites3

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

Cited by23

Results whose statement or proof uses this declaration.