Theorems · Definition · category theory

CategoryTheory.Bicategory.Adj.Bicategory.associator

{B : Type u} →
  [inst : CategoryTheory.Bicategory B] →
    {a b c d : CategoryTheory.Bicategory.Adj B} →
      (α : a ⟶ b) →
        (β : b ⟶ c) →
          (γ : c ⟶ d) →
            CategoryTheory.CategoryStruct.comp (CategoryTheory.CategoryStruct.comp α β) γ ≅
              CategoryTheory.CategoryStruct.comp α (CategoryTheory.CategoryStruct.comp β γ)

The associator in the bicategory Adj B.

Defined in: Mathlib.CategoryTheory.Bicategory.Adjunction.Adj
Cited by: 4 results in Mathlib
Foundations: Depth 38 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Bicategory

Mathlib docs Source Loogle LeanSearch

Around this declaration

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

Cites9

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.Isostatement · cited by 3,963
CategoryTheory.Bicategorystatement and proof · cited by 1,587
CategoryTheory.Bicategory.associatorproof · cited by 405
CategoryTheory.Bicategory.Adjstatement and proof · cited by 131
CategoryTheory.Bicategory.Adj.Hom.lproof · cited by 89
CategoryTheory.Bicategory.Adj.Hom.rproof · cited by 82
CategoryTheory.Bicategory.Adj.iso₂Mkproof · cited by 5

Cited by4

Results whose statement or proof uses this declaration.

CategoryTheory.Bicategory.Adj.Bicategory.associator_hom_τlstatement and proof · cited by 0
CategoryTheory.Bicategory.Adj.Bicategory.associator_hom_τrstatement and proof · cited by 0
CategoryTheory.Bicategory.Adj.Bicategory.associator_inv_τlstatement and proof · cited by 0
CategoryTheory.Bicategory.Adj.Bicategory.associator_inv_τrstatement and proof · cited by 0