Theorems · Definition · category theory

CategoryTheory.Limits.MulticospanIndex.parallelPairDiagram

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

Defined in

Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer

Cited by

2 results in Mathlib

Foundations

Depth 27 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasProductCategoryTheory.Limits.HasProduct