Mathlib Map

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 C

The equivalence C ≅ Karoubi C when C is idempotent complete.

Defined in
Mathlib.CategoryTheory.Idempotents.Karoubi
Cited by
14 results in Mathlib
Foundations
Depth 26 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.IsIdempotentComplete

Around this declaration

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

CategoryTheory.Idempotents.DoldKan.N · cited by 7DoldKan.NCategoryTheory.Idempotents.functorExtension · cited by 4Idempotents.functorExtens…CategoryTheory.Idempotents.DoldKan.isoN₁ · cited by 3DoldKan.isoN₁CategoryTheory.Idempotents.DoldKan.isoΓ₀ · cited by 2DoldKan.isoΓ₀CategoryTheory.Abelian.DoldKan.comparisonN · cited by 2DoldKan.comparisonNCategoryTheory.Idempotents.DoldKan.hε · cited by 1DoldKan.hεCategoryTheory.Idempotents.DoldKan.hη · cited by 1DoldKan.hηCategoryTheory.Idempotents.DoldKan.N₂_map_isoΓ₀_hom_app_f · cited by 1DoldKan.N₂_map_isoΓ₀_hom_…CategoryTheory.Idempotents.DoldKan.isoN₁_hom_app_f · cited by 0DoldKan.isoN₁_hom_app_fCategoryTheory.Abelian.DoldKan.comparisonN_hom_app_f · cited by 0DoldKan.comparisonN_hom_a…CategoryTheory.Abelian.DoldKan.comparisonN_inv_app_f · cited by 0DoldKan.comparisonN_inv_a…CategoryTheory.Idempotents.DoldKan.η_hom_app_f · cited by 0DoldKan.η_hom_app_fCategoryTheory.Idempotents.DoldKan.η_inv_app_f · cited by 0DoldKan.η_inv_app_fCategoryTheory.Idempotents.functorExtension_map_app · cited by 0Idempotents.functorExtens…CategoryTheory.Idempotents.functorExtension_obj_map · cited by 0Idempotents.functorExtens…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.Equivalence · cited by 601CategoryTheory.EquivalenceCategoryTheory.Idempotents.Karoubi · cited by 233Idempotents.KaroubiCategoryTheory.Idempotents.toKaroubi · cited by 69Idempotents.toKaroubiCategoryTheory.Functor.asEquivalence · cited by 58Functor.asEquivalenceCategoryTheory.IsIdempotentComplete · cited by 29CategoryTheory.IsIdempote…Idempotents.toKaroubiEquivale…CITED BYCITES

Cites6

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

Cited by20

Results whose statement or proof uses this declaration.