Theorems · Definition · category theory

CategoryTheory.Limits.cospan

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

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

Defined in: Mathlib.CategoryTheory.Limits.Shapes.Pullback.Cospan
Cited by: 467 results in Mathlib
Foundations: Depth 16 from the axioms, rests on 85 definitions · uses no axioms
Assumes: CategoryTheory.Category

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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.WalkingCospanstatement · cited by 496
CategoryTheory.Limits.WalkingPair.casesOnproof · cited by 59
CategoryTheory.Limits.WidePullbackShape.wideCospanproof · cited by 22

Cited by653

Results whose statement or proof uses this declaration.

CategoryTheory.Limits.pullbackproof · cited by 864
CategoryTheory.Limits.pullback.fstproof · cited by 639
CategoryTheory.Limits.pullback.sndproof · cited by 637
CategoryTheory.Limits.HasPullbackproof · cited by 434
CategoryTheory.Limits.PullbackConeproof · cited by 136
CategoryTheory.Limits.pullback.conditionproof · cited by 122
CategoryTheory.Limits.PullbackCone.mk_π_appstatement · cited by 120
CategoryTheory.Limits.PullbackCone.fststatement · cited by 118
CategoryTheory.Limits.pullback.liftproof · cited by 114
CategoryTheory.Limits.PullbackCone.sndstatement · cited by 113
CategoryTheory.IsPullback.of_hasPullbackproof · cited by 70
CategoryTheory.Limits.pullback.hom_extproof · cited by 63

Showing the 200 most cited of 653.