Theorems · Definition · category theory

CategoryTheory.Bicategory.LeftLift.homMk

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

To construct a morphism between left lifts, we need a 2-morphism between the lifts, 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