Theorems · Definition · category theory

CategoryTheory.Limits.MultispanIndex.map

{C : Type u_1} →
  {D : Type u_2} →
    [inst : CategoryTheory.Category.{v_1, u_1} C] →
      [inst_1 : CategoryTheory.Category.{v_2, u_2} D] →
        {J : CategoryTheory.Limits.MultispanShape} →
          CategoryTheory.Limits.MultispanIndex J C →
            CategoryTheory.Functor C D → CategoryTheory.Limits.MultispanIndex J D

The multispan index obtained by applying a functor.

Defined in: Mathlib.CategoryTheory.Limits.Preserves.Shapes.Multiequalizer
Cited by: 22 results in Mathlib
Foundations: Depth 4 from the axioms · uses no axioms
Assumes: CategoryTheory.Category CategoryTheory.Category

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

Cites12

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.Functor.objproof · cited by 19,642
CategoryTheory.Functorstatement and proof · cited by 16,252
CategoryTheory.Functor.mapproof · cited by 8,698
CategoryTheory.Limits.MultispanShape.Rproof · cited by 133
CategoryTheory.Limits.MultispanShape.Lproof · cited by 129
CategoryTheory.Limits.MultispanIndex.rightproof · cited by 117
CategoryTheory.Limits.MultispanIndexstatement and proof · cited by 102
CategoryTheory.Limits.MultispanShapestatement and proof · cited by 102
CategoryTheory.Limits.MultispanIndex.leftproof · cited by 85
CategoryTheory.Limits.MultispanIndex.fstproof · cited by 40
CategoryTheory.Limits.MultispanIndex.sndproof · cited by 40

Cited by33

Results whose statement or proof uses this declaration.

SSet.horn₃₁.desc.multicoforkstatement and proof · cited by 10
SSet.horn₃₂.desc.multicoforkstatement and proof · cited by 10
SSet.horn.isColimitstatement · cited by 8
CategoryTheory.Limits.Multicofork.mapstatement and proof · cited by 4
CategoryTheory.Limits.MultispanIndex.multispanMapIsostatement and proof · cited by 2
SSet.horn₃₁.desc.multicofork_π_threestatement · cited by 1
SSet.horn₃₁.desc.multicofork_π_twostatement · cited by 1
CategoryTheory.Limits.Types.isColimitOfMulticoequalizerDiagram'statement · cited by 1
CategoryTheory.Limits.Multicofork.map_ι_appstatement · cited by 1
SSet.horn₃₁.desc.multicofork_π_zerostatement · cited by 1
SSet.horn₃₂.desc.multicofork_π_onestatement · cited by 1
SSet.horn₃₂.desc.multicofork_π_threestatement · cited by 1