Theorems · Definition · category theory

CategoryTheory.Bicategory.LeftExtension.homMk

{B : Type u} →
  [inst : CategoryTheory.Bicategory B] →
    {a b c : B} →
      {f : a ⟶ b} →
        {g : a ⟶ c} →
          {s t : CategoryTheory.Bicategory.LeftExtension f g} →
            (η : s.extension ⟶ t.extension) →
              autoParam (CategoryTheory.CategoryStruct.comp s.unit (CategoryTheory.Bicategory.whiskerLeft f η) = t.unit)
                  CategoryTheory.Bicategory.LeftExtension.homMk._auto_1 →
                (s ⟶ t)

To construct a morphism between left extensions, we need a 2-morphism between the extensions, and to check that it is compatible with the units.

Defined in

Mathlib.CategoryTheory.Bicategory.Extension

Cited by

2 results in Mathlib

Foundations

Depth 28 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.Bicategory