Theorems · Definition · category theory
CategoryTheory.ShrinkHoms.equivalence
(C : Type u) →
[inst : CategoryTheory.Category.{v, u} C] →
[inst_1 : CategoryTheory.LocallySmall.{w, v, u} C] → C ≌ CategoryTheory.ShrinkHoms.{u} CThe categorical equivalence between C and ShrinkHoms C, when C is locally small.
- Defined in
- Mathlib.CategoryTheory.EssentiallySmall
- Cited by
- 26 results in Mathlib
- Foundations
- Depth 25 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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.Functor.idproof · cited by 3,333
- CategoryTheory.Iso.reflproof · cited by 727
- CategoryTheory.Equivalencestatement · cited by 601
- CategoryTheory.LocallySmallstatement and proof · cited by 242
- CategoryTheory.NatIso.ofComponentsproof · cited by 178
- CategoryTheory.ShrinkHomsstatement and proof · cited by 34
- CategoryTheory.ShrinkHoms.inverseproof · cited by 6
- CategoryTheory.ShrinkHoms.functorproof · cited by 5
Cited by33
Results whose statement or proof uses this declaration.
- CategoryTheory.IsCardinalFiltered.coconeproof · cited by 5
- CategoryTheory.ShrinkHoms.equivalence_inversestatement and proof · cited by 2
- CategoryTheory.Limits.hasFilteredColimitsOfSize_of_univLEproof · cited by 2
- CategoryTheory.isCardinalPresentable_of_isColimitproof · cited by 2
- CategoryTheory.Limits.hasCofilteredLimitsOfSize_of_univLEproof · cited by 2
- CategoryTheory.Limits.hasLimitsOfSizeOfUnivLEproof · cited by 1
- CategoryTheory.Limits.reflectsLimitsOfSize_of_univLEproof · cited by 1
- CategoryTheory.Limits.HasColimitsOfShape.of_smallproof · cited by 1
- CategoryTheory.Limits.hasColimitsOfSizeOfUnivLEproof · cited by 1
- CategoryTheory.Arrow.shrinkHomsEquivproof · cited by 1
- CategoryTheory.Limits.preservesFilteredColimitsOfSize_of_univLEproof · cited by 1
- CategoryTheory.ObjectProperty.ind_indproof · cited by 1