Theorems · Definition · category theory
CategoryTheory.Shrink.equivalence
(C : Type u) → [inst : CategoryTheory.Category.{v, u} C] → [inst_1 : Small.{w, u} C] → C ≌ Shrink.{w, u} CThe categorical equivalence between C and Shrink C, when C is small.
- Defined in
- Mathlib.CategoryTheory.EssentiallySmall
- Cited by
- 18 results in Mathlib
- Foundations
- Depth 27 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CategoryTheory.CategorySmall
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- Equiv.symmproof · cited by 3,681
- CategoryTheory.Equivalencestatement · cited by 601
- Smallstatement and proof · cited by 369
- CategoryTheory.Equivalence.symmproof · cited by 195
- Shrinkstatement · cited by 132
- equivShrinkproof · cited by 118
- CategoryTheory.Equivalence.inducedproof · cited by 5
Cited by22
Results whose statement or proof uses this declaration.
- CategoryTheory.IsCardinalFiltered.coconeproof · cited by 5
- CategoryTheory.Limits.hasCofilteredLimitsOfSize_of_univLEproof · cited by 2
- CategoryTheory.Limits.hasFilteredColimitsOfSize_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.Limits.reflectsFilteredColimitsOfSize_of_univLEproof · cited by 1
- CategoryTheory.Arrow.shrinkEquivproof · cited by 1
- CategoryTheory.Limits.preservesCofilteredLimitsOfSize_of_univLEproof · cited by 1
- CategoryTheory.Limits.preservesFilteredColimitsOfSize_of_univLEproof · cited by 1
- CategoryTheory.ObjectProperty.exists_equivalence_iffproof · cited by 1