Theorems · Definition · category theory
CategoryTheory.Idempotents.toKaroubiEquivalence
(C : Type u_1) →
[inst : CategoryTheory.Category.{v_1, u_1} C] →
[CategoryTheory.IsIdempotentComplete C] → C ≌ CategoryTheory.Idempotents.Karoubi CThe equivalence C ≅ Karoubi C when C is idempotent complete.
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- CategoryTheory.Idempotents.Karoubistatement · cited by 233
- CategoryTheory.Idempotents.toKaroubiproof · cited by 69
- CategoryTheory.Functor.asEquivalenceproof · cited by 58
- CategoryTheory.IsIdempotentCompletestatement and proof · cited by 29
Cited by20
Results whose statement or proof uses this declaration.
- CategoryTheory.Idempotents.DoldKan.Nproof · cited by 7
- CategoryTheory.Idempotents.functorExtensionproof · cited by 4
- CategoryTheory.Idempotents.DoldKan.isoN₁statement · cited by 3
- CategoryTheory.Idempotents.DoldKan.isoΓ₀statement · cited by 2
- CategoryTheory.Abelian.DoldKan.comparisonNproof · cited by 2
- CategoryTheory.Idempotents.DoldKan.hεstatement and proof · cited by 1
- CategoryTheory.Idempotents.DoldKan.hηstatement · cited by 1
- CategoryTheory.Idempotents.DoldKan.N₂_map_isoΓ₀_hom_app_fstatement · cited by 1
- CategoryTheory.Idempotents.DoldKan.isoN₁_hom_app_fstatement · cited by 0
- CategoryTheory.Abelian.DoldKan.comparisonN_hom_app_fstatement and proof · cited by 0
- CategoryTheory.Abelian.DoldKan.comparisonN_inv_app_fstatement and proof · cited by 0
- CategoryTheory.Idempotents.DoldKan.η_hom_app_fstatement and proof · cited by 0