Theorems · Definition · category theory

CategoryTheory.Bicategory.Adjunction.compUnit

{B : Type u₁} →
  [inst : CategoryTheory.Bicategory B] →
    {a b c : B} →
      {f₁ : a ⟶ b} →
        {g₁ : b ⟶ a} →
          {f₂ : b ⟶ c} →
            {g₂ : c ⟶ b} →
              CategoryTheory.Bicategory.Adjunction f₁ g₁ →
                CategoryTheory.Bicategory.Adjunction f₂ g₂ →
                  (CategoryTheory.CategoryStruct.id a ⟶
                    CategoryTheory.CategoryStruct.comp (CategoryTheory.CategoryStruct.comp f₁ f₂)
                      (CategoryTheory.CategoryStruct.comp g₂ g₁))

Auxiliary definition for Adjunction.comp.

Defined in: Mathlib.CategoryTheory.Bicategory.Adjunction.Basic
Cited by: 3 results in Mathlib
Foundations: Depth 17 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Bicategory

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

Cites8

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 and proof · cited by 17,999
CategoryTheory.CategoryStruct.idstatement and proof · cited by 6,235
CategoryTheory.Bicategorystatement and proof · cited by 1,587
CategoryTheory.Bicategory.whiskerRightproof · cited by 531
CategoryTheory.Bicategory.whiskerLeftproof · cited by 524
CategoryTheory.Bicategory.Adjunctionstatement and proof · cited by 83
CategoryTheory.Bicategory.Adjunction.unitproof · cited by 48

Cited by4

Results whose statement or proof uses this declaration.

CategoryTheory.Bicategory.Adjunction.compproof · cited by 16
CategoryTheory.Bicategory.Adjunction.comp_unitstatement · cited by 1
CategoryTheory.Bicategory.Adjunction.comp_left_triangle_auxstatement · cited by 0
CategoryTheory.Bicategory.Adjunction.comp_right_triangle_auxstatement · cited by 0