Theorems · Definition · category theory

CategoryTheory.Limits.Multifork.toPiFork

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    {J : CategoryTheory.Limits.MulticospanShape} →
      {I : CategoryTheory.Limits.MulticospanIndex J C} →
        {c : CategoryTheory.Limits.Fan I.left} →
          CategoryTheory.Limits.IsLimit c →
            {d : CategoryTheory.Limits.Fan I.right} →
              (hd : CategoryTheory.Limits.IsLimit d) →
                CategoryTheory.Limits.Multifork I →
                  CategoryTheory.Limits.Fork (I.fstPiMapOfIsLimit c hd) (I.sndPiMapOfIsLimit c hd)

Given a multifork, we may obtain a fork over ∏ᶜ I.left ⇉ ∏ᶜ I.right.

Defined in: Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
Cited by: 6 results in Mathlib
Foundations: Depth 30 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category

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Dashed lines are statement dependencies; solid lines are citations in proofs.

Cites19

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

CategoryTheory.Categorystatement and proof · cited by 32,673
CategoryTheory.Discretestatement · cited by 2,447
CategoryTheory.Limits.Cone.ptstatement · cited by 1,298
CategoryTheory.Limits.IsLimitstatement and proof · cited by 664
CategoryTheory.Discrete.functorstatement · cited by 633
CategoryTheory.Limits.MulticospanShapestatement and proof · cited by 160
CategoryTheory.Limits.MulticospanShape.Lstatement · cited by 135
CategoryTheory.Limits.MulticospanShape.Rstatement · cited by 124
CategoryTheory.Limits.MulticospanIndex.leftstatement and proof · cited by 119
CategoryTheory.Limits.MulticospanIndexstatement and proof · cited by 101
CategoryTheory.Limits.Forkstatement · cited by 85
CategoryTheory.Limits.MulticospanIndex.rightstatement and proof · cited by 77

Cited by7

Results whose statement or proof uses this declaration.

CategoryTheory.Limits.MulticospanIndex.toPiForkFunctorproof · cited by 9
CategoryTheory.Limits.MulticospanIndex.toPiForkFunctor_map_homstatement · cited by 0
CategoryTheory.Limits.MulticospanIndex.toPiForkFunctor_objstatement · cited by 0
CategoryTheory.Limits.Multifork.toPiFork_ptstatement and proof · cited by 0
CategoryTheory.Limits.Multifork.toPiFork_π_app_onestatement · cited by 0
CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_functor_map_homstatement · cited by 0
CategoryTheory.Limits.Multifork.toPiFork_π_app_zerostatement · cited by 0