Theorems · Definition · category theory

CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiForkOfIsLimit

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    {J : CategoryTheory.Limits.MulticospanShape} →
      (I : CategoryTheory.Limits.MulticospanIndex J C) →
        {c : CategoryTheory.Limits.Fan I.left} →
          CategoryTheory.Limits.IsLimit c →
            {d : CategoryTheory.Limits.Fan I.right} →
              (hd : CategoryTheory.Limits.IsLimit d) →
                CategoryTheory.Limits.Multifork I ≌
                  CategoryTheory.Limits.Fork (I.fstPiMapOfIsLimit c hd) (I.sndPiMapOfIsLimit c hd)

The category of multiforks is equivalent to the category of forks over ∏ᶜ I.left ⇉ ∏ᶜ I.right. It then follows from CategoryTheory.IsLimit.ofPreservesConeTerminal (or reflects) that it preserves and reflects limit cones.

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