Theorems · Definition · category theory
CategoryTheory.Bicategory.Adjunction.unit
{B : Type u₁} →
[inst : CategoryTheory.Bicategory B] →
{a b : B} →
{f : a ⟶ b} →
{g : b ⟶ a} →
CategoryTheory.Bicategory.Adjunction f g →
(CategoryTheory.CategoryStruct.id a ⟶ CategoryTheory.CategoryStruct.comp f g)The unit of an adjunction.
- Cited by
- 48 results in Mathlib
- Foundations
- Depth 3 from the axioms · uses no axioms
- Assumes
- CategoryTheory.Bicategory
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.CategoryStruct.compstatement · cited by 17,999
- CategoryTheory.CategoryStruct.idstatement · cited by 6,235
- CategoryTheory.Bicategorystatement and proof · cited by 1,587
- CategoryTheory.Bicategory.Adjunctionstatement and proof · cited by 83
Cited by62
Results whose statement or proof uses this declaration.
- CategoryTheory.Adjunction.ofCatproof · cited by 25
- CategoryTheory.Bicategory.mateEquiv_apply'statement and proof · cited by 9
- CategoryTheory.Bicategory.Adjunction.homEquiv₁proof · cited by 7
- CategoryTheory.Pseudofunctor.toDescentDataAsCoalgebraproof · cited by 6
- CategoryTheory.Bicategory.Adjunction.homEquiv₂proof · cited by 5
- CategoryTheory.Bicategory.mateEquiv_vcompproof · cited by 4
- CategoryTheory.Bicategory.conjugateEquiv_idproof · cited by 3
- CategoryTheory.Bicategory.mateEquiv_hcompproof · cited by 3
- CategoryTheory.Bicategory.Adjunction.compUnitproof · cited by 3
- CategoryTheory.Bicategory.conjugateEquiv_compproof · cited by 2
- CategoryTheory.Pseudofunctor.mapAdjunctionproof · cited by 2
- CategoryTheory.Bicategory.mateEquiv_symm_apply'statement and proof · cited by 2