Theorems · Definition · category theory

CategoryTheory.Limits.MultispanIndex.parallelPairDiagramOfIsColimit

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    {J : CategoryTheory.Limits.MultispanShape} →
      (I : CategoryTheory.Limits.MultispanIndex J C) →
        {c : CategoryTheory.Limits.Cofan I.left} →
          CategoryTheory.Limits.Cofan I.right →
            CategoryTheory.Limits.IsColimit c → CategoryTheory.Functor CategoryTheory.Limits.WalkingParallelPair C

Taking the multicoequalizer over the multispan index is equivalent to taking the coequalizer over the two morphisms ∐ I.left ⇉ ∐ I.right. This is the diagram of the latter for colimiting cofans.

Defined in

Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer

Cited by

2 results in Mathlib

Foundations

Depth 26 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.Category