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Theorems · Definition · category theory

CategoryTheory.Bicategory.Adjunction.counit

{B : Type u₁} →
  [inst : CategoryTheory.Bicategory B] →
    {a b : B} →
      {f : a ⟶ b} →
        {g : b ⟶ a} →
          CategoryTheory.Bicategory.Adjunction f g →
            (CategoryTheory.CategoryStruct.comp g f ⟶ CategoryTheory.CategoryStruct.id b)

The counit of an adjunction.

Defined in
Mathlib.CategoryTheory.Bicategory.Adjunction.Basic
Cited by
44 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.

CategoryTheory.Adjunction.ofCat · cited by 25Adjunction.ofCatCategoryTheory.Bicategory.mateEquiv_apply' · cited by 9Bicategory.mateEquiv_appl…CategoryTheory.Bicategory.Adjunction.homEquiv₁ · cited by 7Adjunction.homEquiv₁CategoryTheory.Bicategory.Adjunction.homEquiv₂ · cited by 5Adjunction.homEquiv₂CategoryTheory.Bicategory.mateEquiv_vcomp · cited by 4Bicategory.mateEquiv_vcompCategoryTheory.Bicategory.conjugateEquiv_id · cited by 3Bicategory.conjugateEquiv…CategoryTheory.Bicategory.mateEquiv_hcomp · cited by 3Bicategory.mateEquiv_hcompCategoryTheory.Bicategory.Adjunction.compCounit · cited by 3Adjunction.compCounitCategoryTheory.Bicategory.conjugateEquiv_comp · cited by 2Bicategory.conjugateEquiv…CategoryTheory.Pseudofunctor.mapAdjunction · cited by 2Pseudofunctor.mapAdjuncti…CategoryTheory.Bicategory.mateEquiv_symm_apply' · cited by 2Bicategory.mateEquiv_symm…CategoryTheory.Bicategory.Adjunction.ext · cited by 2Adjunction.extCategoryTheory.Bicategory.Adjunction.left_triangle · cited by 2Adjunction.left_triangleCategoryTheory.Bicategory.Adjunction.right_triangle · cited by 2Adjunction.right_triangleCategoryTheory.StrictPseudofunctor.mapAdjunction_counit · cited by 1StrictPseudofunctor.mapAd…Quiver.Hom · cited by 32603Quiver.HomCategoryTheory.CategoryStruct.comp · cited by 17999CategoryStruct.compCategoryTheory.CategoryStruct.id · cited by 6235CategoryStruct.idCategoryTheory.Bicategory · cited by 1587CategoryTheory.BicategoryCategoryTheory.Bicategory.Adjunction · cited by 83Bicategory.AdjunctionAdjunction.counitCITED BYCITES

Cites5

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Cited by56

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