Theorems · Definition · category theory

CategoryTheory.Limits.pushoutSymmetry

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    {X Y Z : C} →
      (f : X ⟶ Y) →
        (g : X ⟶ Z) →
          [inst_1 : CategoryTheory.Limits.HasPushout f g] →
            CategoryTheory.Limits.pushout f g ≅ CategoryTheory.Limits.pushout g f

The isomorphism Y ⨿[X] Z ≅ Z ⨿[X] Y.

Defined in: Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback
Cited by: 30 results in Mathlib
Foundations: Depth 32 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Limits.HasPushout

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Around this declaration

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

Cites11

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.Isostatement · cited by 3,963
CategoryTheory.Limits.spanproof · cited by 294
CategoryTheory.Limits.pushoutstatement · cited by 284
CategoryTheory.Limits.colimit.isColimitproof · cited by 193
CategoryTheory.Limits.HasPushoutstatement and proof · cited by 192
CategoryTheory.Limits.IsColimit.coconePointUniqueUpToIsoproof · cited by 67
CategoryTheory.Limits.hasPushout_symmetrystatement · cited by 18
CategoryTheory.Limits.pushoutIsPushoutproof · cited by 7
CategoryTheory.Limits.PushoutCocone.flipIsColimitproof · cited by 6

Cited by31

Results whose statement or proof uses this declaration.

CategoryTheory.MonoidalCategory.Arrow.PushoutProduct.braidingproof · cited by 12
CategoryTheory.Limits.inl_comp_pushoutSymmetry_hom_assocstatement and proof · cited by 8
CategoryTheory.Limits.inr_comp_pushoutSymmetry_hom_assocstatement and proof · cited by 7
CategoryTheory.Limits.inr_comp_pushoutSymmetry_homstatement · cited by 5
CategoryTheory.Limits.inl_comp_pushoutSymmetry_homstatement · cited by 4
CategoryTheory.MonoidalCategory.Limits.whiskerLeft_inl_comp_pushoutSymmetry_hom_assocstatement and proof · cited by 3
CategoryTheory.MonoidalCategory.Limits.inl_comp_pushoutSymmetry_hom_whiskerRight_assocstatement and proof · cited by 2
CategoryTheory.MonoidalCategory.Limits.inr_comp_pushoutSymmetry_hom_whiskerRight_assocstatement and proof · cited by 2
CategoryTheory.MonoidalCategory.Limits.whiskerLeft_inr_comp_pushoutSymmetry_hom_assocstatement and proof · cited by 2
CategoryTheory.MonoidalCategory.Limits.inl_comp_pushoutSymmetry_hom_whiskerRightstatement and proof · cited by 1
CategoryTheory.MonoidalCategory.Limits.inr_comp_pushoutSymmetry_hom_whiskerRightstatement and proof · cited by 1
CategoryTheory.MonoidalCategory.Limits.whiskerLeft_inl_comp_pushoutSymmetry_homstatement and proof · cited by 1