Theorems · Definition · category theory

CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    {J : CategoryTheory.Limits.MulticospanShape} →
      (I : CategoryTheory.Limits.MulticospanIndex J C) →
        [inst_1 : CategoryTheory.Limits.HasProduct I.left] →
          [inst_2 : CategoryTheory.Limits.HasProduct I.right] →
            CategoryTheory.Limits.Multifork I ≌ CategoryTheory.Limits.Fork I.fstPiMap I.sndPiMap

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

11 results in Mathlib

Foundations

Depth 38 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasProductCategoryTheory.Limits.HasProduct