Theorems · Definition · category theory

CategoryTheory.Limits.PushoutCocone.inl

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    {X Y Z : C} → {f : X ⟶ Y} → {g : X ⟶ Z} → (t : CategoryTheory.Limits.PushoutCocone f g) → Y ⟶ t.pt

The first inclusion of a pushout cocone.

Defined in: Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackCone
Cited by: 58 results in Mathlib
Foundations: Depth 23 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category

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

Cites10

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.NatTrans.appproof · cited by 7,406
CategoryTheory.Limits.Cocone.ptstatement · cited by 1,354
CategoryTheory.Limits.WalkingPairstatement · cited by 1,319
CategoryTheory.Limits.Cocone.ιproof · cited by 605
CategoryTheory.Limits.WalkingSpanstatement · cited by 300
CategoryTheory.Limits.spanstatement · cited by 294
CategoryTheory.Limits.WalkingSpan.leftproof · cited by 80
CategoryTheory.Limits.PushoutCoconestatement and proof · cited by 66

Cited by92

Results whose statement or proof uses this declaration.

CategoryTheory.Limits.PushoutCocone.conditionstatement · cited by 15
CategoryTheory.IsPushout.of_isColimitstatement and proof · cited by 9
CategoryTheory.Limits.PushoutCocone.IsColimit.mkstatement and proof · cited by 8
CategoryTheory.Limits.pushoutCoconeEquivBinaryCofanproof · cited by 7
CategoryTheory.Limits.pushoutIsPushoutproof · cited by 7
CategoryTheory.Limits.PushoutCocone.flipIsColimitproof · cited by 6
CategoryTheory.Limits.PushoutCocone.IsColimit.hom_extstatement and proof · cited by 6
CommRingCat.pushoutCoconeIsColimitproof · cited by 5
CategoryTheory.Limits.pasteHorizIsPushoutproof · cited by 5
CategoryTheory.Limits.pasteVertIsPushoutstatement and proof · cited by 4
CategoryTheory.Limits.PushoutCocone.condition_zerostatement · cited by 4
CategoryTheory.Limits.PushoutCocone.flipproof · cited by 4