Theorems · Definition · category theory
CategoryTheory.Equivalence.counit
{C : Type u₁} →
[inst : CategoryTheory.Category.{v₁, u₁} C] →
{D : Type u₂} →
[inst_1 : CategoryTheory.Category.{v₂, u₂} D] →
(e : C ≌ D) → e.inverse.comp e.functor ⟶ CategoryTheory.Functor.id DThe counit of an equivalence of categories.
- Defined in
- Mathlib.CategoryTheory.Equivalence
- Cited by
- 52 results in Mathlib
- Foundations
- Depth 21 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
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
- Quiver.Homstatement · cited by 32,603
- CategoryTheory.Functorstatement · cited by 16,252
- CategoryTheory.Iso.homproof · cited by 7,684
- CategoryTheory.Functor.compstatement · cited by 6,529
- CategoryTheory.Functor.idstatement · cited by 3,333
- CategoryTheory.Equivalence.functorstatement · cited by 1,268
- CategoryTheory.Equivalence.inversestatement · cited by 1,130
- CategoryTheory.Equivalencestatement and proof · cited by 601
- CategoryTheory.Equivalence.counitIsoproof · cited by 480
Cited by55
Results whose statement or proof uses this declaration.
- CategoryTheory.Equivalence.toAdjunctionproof · cited by 60
- CategoryTheory.Equivalence.fun_inv_mapstatement · cited by 9
- CategoryTheory.Equivalence.invFunIdAssoc_hom_appstatement and proof · cited by 7
- CategoryTheory.Equivalence.functor_unit_compstatement · cited by 6
- CategoryTheory.Limits.preservesLimitsOfShape_of_equivproof · cited by 6
- CategoryTheory.Limits.HasLimit.isoOfEquivalence_hom_πstatement and proof · cited by 4
- CategoryTheory.Equivalence.counit_naturalitystatement and proof · cited by 3
- CategoryTheory.Equivalence.unit_inverse_compstatement and proof · cited by 3
- CategoryTheory.Equivalence.inverse_counitInv_compproof · cited by 2
- CategoryTheory.Limits.Pi.reindex_hom_πproof · cited by 2
- CategoryTheory.Equivalence.counit_app_functorstatement and proof · cited by 2
- SheafOfModules.pushforwardPushforwardEquivalencestatement and proof · cited by 2