Theorems · Definition · category theory

CategoryTheory.Limits.span

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    {X Y Z : C} → (X ⟶ Y) → (X ⟶ Z) → CategoryTheory.Functor CategoryTheory.Limits.WalkingSpan C

span f g is the functor from the walking span hitting f and g.

Defined in: Mathlib.CategoryTheory.Limits.Shapes.Pullback.Cospan
Cited by: 294 results in Mathlib
Foundations: Depth 16 from the axioms, rests on 85 definitions · uses no axioms
Assumes: CategoryTheory.Category

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

Cites7

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 and proof · cited by 32,603
CategoryTheory.Functorstatement · cited by 16,252
CategoryTheory.Limits.WalkingPairstatement and proof · cited by 1,319
CategoryTheory.Limits.WalkingSpanstatement · cited by 300
CategoryTheory.Limits.WalkingPair.casesOnproof · cited by 59
CategoryTheory.Limits.WidePushoutShape.wideSpanproof · cited by 8

Cited by399

Results whose statement or proof uses this declaration.

CategoryTheory.Limits.pushoutproof · cited by 284
CategoryTheory.Limits.pushout.inrproof · cited by 193
CategoryTheory.Limits.HasPushoutproof · cited by 192
CategoryTheory.Limits.pushout.inlproof · cited by 192
CategoryTheory.Limits.PushoutCoconeproof · cited by 66
CategoryTheory.Limits.PushoutCocone.inlstatement · cited by 58
CategoryTheory.Limits.PushoutCocone.inrstatement · cited by 58
CategoryTheory.Limits.pushout.descproof · cited by 46
CategoryTheory.Limits.pushoutSymmetryproof · cited by 30
CategoryTheory.Limits.PushoutCocone.mk_ι_appstatement · cited by 30
CategoryTheory.IsPushout.isColimitstatement · cited by 30
CategoryTheory.Limits.pushout.hom_extproof · cited by 30

Showing the 200 most cited of 399.