Theorems · Definition · category theory

CategoryTheory.Limits.MulticospanIndex.parallelPairDiagramOfIsLimit

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    {J : CategoryTheory.Limits.MulticospanShape} →
      (I : CategoryTheory.Limits.MulticospanIndex J C) →
        CategoryTheory.Limits.Fan I.left →
          {d : CategoryTheory.Limits.Fan I.right} →
            CategoryTheory.Limits.IsLimit d → CategoryTheory.Functor CategoryTheory.Limits.WalkingParallelPair C

Taking the multiequalizer over the multicospan index is equivalent to taking the equalizer over the two morphisms ∏ᶜ I.left ⇉ ∏ᶜ I.right. This is the diagram of the latter for limiting fans.

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