Theorems · Theorem · category theory

CategoryTheory.Bicategory.Strict.assoc

∀ {B : Type u} {inst : CategoryTheory.Bicategory B} [self : CategoryTheory.Bicategory.Strict B] {a b c d : B}
  (f : a ⟶ b) (g : b ⟶ c) (h : c ⟶ d),
  CategoryTheory.CategoryStruct.comp (CategoryTheory.CategoryStruct.comp f g) h =
    CategoryTheory.CategoryStruct.comp f (CategoryTheory.CategoryStruct.comp g h)

Composition in a bicategory is associative.

Defined in: Mathlib.CategoryTheory.Bicategory.Strict.Basic
Cited by: 3 results in Mathlib
Foundations: Depth 3 from the axioms · uses no axioms
Assumes: CategoryTheory.Bicategory.Strict

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Cites4

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Quiver.Homstatement · cited by 32,603
CategoryTheory.CategoryStruct.compstatement · cited by 17,999
CategoryTheory.Bicategorystatement and proof · cited by 1,587
CategoryTheory.Bicategory.Strictstatement and proof · cited by 87

Cited by3

Results whose statement or proof uses this declaration.

CategoryTheory.Bicategory.Strict.associator_eqToIsostatement · cited by 5
CategoryTheory.Pseudofunctor.mapComp'₀₁₃_hom_comp_whiskerLeft_mapComp'_homproof · cited by 2
CategoryTheory.OplaxFunctor.mapComp'_comp_whiskerLeft_mapComp'proof · cited by 1