Theorems · Definition · category theory

CategoryTheory.Limits.diagramIsoParallelFamily

{J : Type w} →
  {C : Type u} →
    [inst : CategoryTheory.Category.{v, u} C] →
      (F : CategoryTheory.Functor (CategoryTheory.Limits.WalkingParallelFamily J) C) →
        F ≅ CategoryTheory.Limits.parallelFamily fun j => F.map (CategoryTheory.Limits.WalkingParallelFamily.Hom.line j)

Every functor indexing a wide (co)equalizer is naturally isomorphic (actually, equal) to a parallelFamily

Defined in

Mathlib.CategoryTheory.Limits.Shapes.WideEqualizers

Cited by

4 results in Mathlib

Foundations

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

Assumes

CategoryTheory.Category