Theorems · Definition · category theory

CategoryTheory.Bicategory.associatorNatIsoMiddleCat

{B : Type u} →
  [inst : CategoryTheory.Bicategory B] →
    {a b c d : B} →
      (f : a ⟶ b) →
        (h : c ⟶ d) →
          CategoryTheory.CategoryStruct.comp ((CategoryTheory.Bicategory.precomposingCat a b c).obj f)
              ((CategoryTheory.Bicategory.postcomposingCat a c d).obj h) ≅
            CategoryTheory.CategoryStruct.comp ((CategoryTheory.Bicategory.postcomposingCat b c d).obj h)
              ((CategoryTheory.Bicategory.precomposingCat a b d).obj f)

Middle component of the associator as a 2-isomorphism in Cat.

Defined in

Mathlib.CategoryTheory.Bicategory.Yoneda

Cited by

2 results in Mathlib

Foundations

Depth 30 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.Bicategory