Theorems · Definition · category theory

CategoryTheory.Idempotents.KaroubiKaroubi.counitIso

(C : Type u_1) →
  [inst : CategoryTheory.Category.{v_1, u_1} C] →
    (CategoryTheory.Idempotents.KaroubiKaroubi.inverse C).comp
        (CategoryTheory.Idempotents.toKaroubi (CategoryTheory.Idempotents.Karoubi C)) ≅
      CategoryTheory.Functor.id (CategoryTheory.Idempotents.Karoubi (CategoryTheory.Idempotents.Karoubi C))

The counit isomorphism of the equivalence

Defined in: Mathlib.CategoryTheory.Idempotents.KaroubiKaroubi
Cited by: 3 results in Mathlib
Foundations: Depth 24 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category

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Cites10

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.Functorstatement · cited by 16,252
CategoryTheory.Functor.compstatement · cited by 6,529
CategoryTheory.Isostatement · cited by 3,963
CategoryTheory.Functor.idstatement · cited by 3,333
CategoryTheory.Idempotents.Karoubistatement and proof · cited by 233
CategoryTheory.Idempotents.Karoubi.Hom.fproof · cited by 121
CategoryTheory.Idempotents.Karoubi.pproof · cited by 94
CategoryTheory.Idempotents.toKaroubistatement · cited by 69
CategoryTheory.Idempotents.KaroubiKaroubi.inversestatement · cited by 10

Cited by4

Results whose statement or proof uses this declaration.

CategoryTheory.Idempotents.KaroubiKaroubi.equivalenceproof · cited by 5
CategoryTheory.Idempotents.KaroubiKaroubi.counitIso_hom_app_f_fstatement and proof · cited by 0
CategoryTheory.Idempotents.KaroubiKaroubi.counitIso_inv_app_f_fstatement and proof · cited by 0
CategoryTheory.Idempotents.KaroubiKaroubi.equivalence_counitIsostatement · cited by 0