Theorems · Definition · category theory

CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCoforkOfIsColimit

{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} →
          (hc : CategoryTheory.Limits.IsColimit c) →
            {d : CategoryTheory.Limits.Cofan I.right} →
              CategoryTheory.Limits.IsColimit d →
                (CategoryTheory.Limits.Multicofork I ≌
                  CategoryTheory.Limits.Cofork (I.fstSigmaMapOfIsColimit d hc) (I.sndSigmaMapOfIsColimit d hc))

The category of multicoforks is equivalent to the category of coforks over ∐ I.left ⇉ ∐ I.right. It then follows from CategoryTheory.IsColimit.ofPreservesCoconeInitial (or reflects) that it preserves and reflects colimit cocones.

Defined in

Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer

Cited by

4 results in Mathlib

Foundations

Depth 37 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.Category