Theorems · Definition · category theory

CategoryTheory.IndParallelPairPresentation.parallelPairIsoParallelPairCompIndYoneda

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    {A B : CategoryTheory.Ind C} →
      {f g : A ⟶ B} →
        (P :
            CategoryTheory.IndParallelPairPresentation ((CategoryTheory.Ind.inclusion C).map f)
              ((CategoryTheory.Ind.inclusion C).map g)) →
          CategoryTheory.Limits.parallelPair f g ≅
            (CategoryTheory.Limits.parallelPair P.φ P.ψ).comp (CategoryTheory.Ind.lim P.I)

Given an IndParallelPairPresentation f g, we can understand the parallel pair (f, g) as the colimit of (P.φ, P.ψ) in Ind C.

Defined in

Mathlib.CategoryTheory.Limits.Indization.Category

Cited by

1 results in Mathlib

Foundations

Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.Category