Theorems · Definition · category theory

CategoryTheory.Limits.MulticospanIndex.sndPiMapOfIsLimit

{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) →
          {d : CategoryTheory.Limits.Fan I.right} → CategoryTheory.Limits.IsLimit d → (c.pt ⟶ d.pt)

The induced map ∏ᶜ I.left ⟶ ∏ᶜ I.right via I.snd for limiting fans.

Defined in: Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
Cited by: 29 results in Mathlib
Foundations: Depth 25 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category

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Cites18

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
Quiver.Homstatement · cited by 32,603
CategoryTheory.CategoryStruct.compproof · cited by 17,999
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 and proof · cited by 124
CategoryTheory.Limits.MulticospanIndex.leftstatement and proof · cited by 119
CategoryTheory.Limits.MulticospanIndexstatement and proof · cited by 101

Cited by36

Results whose statement or proof uses this declaration.

CategoryTheory.Limits.MulticospanIndex.sndPiMapproof · cited by 14
CategoryTheory.Limits.MulticospanIndex.ofPiForkFunctorstatement and proof · cited by 9
CategoryTheory.Limits.MulticospanIndex.toPiForkFunctorstatement · cited by 9
CategoryTheory.Limits.Multifork.ofPiForkstatement and proof · cited by 6
CategoryTheory.Limits.Multifork.toPiForkstatement · cited by 6
CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiForkOfIsLimitstatement and proof · cited by 4
CategoryTheory.Limits.MulticospanIndex.sndPiMapOfIsLimit_projstatement · cited by 3
CategoryTheory.Limits.MulticospanIndex.parallelPairDiagramOfIsLimitproof · cited by 2
CategoryTheory.Limits.Multifork.pi_conditionstatement and proof · cited by 2
CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_inverse_obj_π_appstatement and proof · cited by 1
CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiForkOfIsLimit_counitIsostatement · cited by 0
CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiForkOfIsLimit_functorstatement · cited by 0