Theorems · Definition · category theory

CategoryTheory.Limits.Multiequalizer.isoEqualizer

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    {J : CategoryTheory.Limits.MulticospanShape} →
      (I : CategoryTheory.Limits.MulticospanIndex J C) →
        [inst_1 : CategoryTheory.Limits.HasMultiequalizer I] →
          [inst_2 : CategoryTheory.Limits.HasProduct I.left] →
            [inst_3 : CategoryTheory.Limits.HasProduct I.right] →
              CategoryTheory.Limits.multiequalizer I ≅ CategoryTheory.Limits.equalizer I.fstPiMap I.sndPiMap

The multiequalizer is isomorphic to the equalizer of ∏ᶜ I.left ⇉ ∏ᶜ I.right.

Defined in

Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer

Cited by

1 results in Mathlib

Foundations

Depth 40 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasMultiequalizerCategoryTheory.Limits.HasProductCategoryTheory.Limits.HasProduct