Theorems · Definition · category theory

CategoryTheory.ThinSkeleton.mapCompFromThinSkeletonIso

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    {D : Type u₂} →
      [inst_1 : CategoryTheory.Category.{v₂, u₂} D] →
        [inst_2 : Quiver.IsThin C] →
          [inst_3 : Quiver.IsThin D] →
            (F : CategoryTheory.Functor C D) →
              (CategoryTheory.ThinSkeleton.map F).comp (CategoryTheory.ThinSkeleton.fromThinSkeleton D) ≅
                (CategoryTheory.ThinSkeleton.fromThinSkeleton C).comp F

Applying map F and then fromThinSkeleton is isomorphic to first applying fromThinSkeleton and then applying F.

Defined in

Mathlib.CategoryTheory.Skeletal

Cited by

0 results in Mathlib

Foundations

Depth 29 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryQuiver.IsThinQuiver.IsThin