Theorems · Definition · category theory

CategoryTheory.FunctorToTypes.shrinkCompUliftFunctorIso

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    (F : CategoryTheory.Functor C (Type w')) →
      [inst_1 : CategoryTheory.FunctorToTypes.Small.{w, w', v, u} F] →
        [inst_2 : CategoryTheory.FunctorToTypes.Small.{max w w'', w', v, u} F] →
          (CategoryTheory.FunctorToTypes.shrink.{w, w', v, u} F).comp CategoryTheory.uliftFunctor.{w'', w} ≅
            CategoryTheory.FunctorToTypes.shrink.{max w w'', w', v, u} F

Shrinking F to Type w followed by universe lifting is the same as shrinking to Type (max w w').

Defined in

Mathlib.CategoryTheory.ShrinkYoneda

Cited by

2 results in Mathlib

Foundations

Depth 24 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.FunctorToTypes.SmallCategoryTheory.FunctorToTypes.Small