Theorems · Definition · category theory

CategoryTheory.Limits.MulticospanIndex.fstPiMap

{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] → ∏ᶜ I.left ⟶ ∏ᶜ I.right

The induced map ∏ᶜ I.left ⟶ ∏ᶜ I.right via I.fst.

Defined in: Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
Cited by: 14 results in Mathlib
Foundations: Depth 26 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Limits.HasProduct CategoryTheory.Limits.HasProduct

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

Cites14

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.Discrete.functorproof · cited by 633
CategoryTheory.Limits.piObjstatement · cited by 237
CategoryTheory.Limits.MulticospanShapestatement and proof · cited by 160
CategoryTheory.Limits.limit.isLimitproof · cited by 146
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.HasProductstatement and proof · cited by 115
CategoryTheory.Limits.MulticospanIndexstatement and proof · cited by 101
CategoryTheory.Limits.limit.coneproof · cited by 97

Cited by18

Results whose statement or proof uses this declaration.

CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiForkstatement · cited by 11
CategoryTheory.Limits.Multiequalizer.ιPiproof · cited by 3
CategoryTheory.Limits.MulticospanIndex.parallelPairDiagramproof · cited by 2
CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_inverse_obj_π_appstatement · cited by 1
CategoryTheory.Limits.Multiequalizer.isoEqualizerstatement and proof · cited by 1
CategoryTheory.Limits.Multiequalizer.ιPi_πproof · cited by 1
CategoryTheory.Limits.MulticospanIndex.fstPiMap_πstatement · cited by 1
CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_counitIso_hom_app_homstatement · cited by 0
CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_counitIso_inv_app_homstatement · cited by 0
CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_functor_map_homstatement · cited by 0
CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_functor_obj_ptstatement · cited by 0
CategoryTheory.Limits.MulticospanIndex.multiforkEquivPiFork_functor_obj_π_appstatement · cited by 0