Theorems · Definition · category theory

CategoryTheory.Limits.PushoutCocone.flipIsColimit

{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} →
            CategoryTheory.Limits.IsColimit t → CategoryTheory.Limits.IsColimit t.flip

The flip of a pushout square is a pushout square.

Defined in: Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackCone
Cited by: 6 results in Mathlib
Foundations: Depth 29 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.

Cites14

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.CategoryStruct.compproof · cited by 17,999
CategoryTheory.Limits.Cocone.ptproof · cited by 1,354
CategoryTheory.Limits.WalkingPairstatement · cited by 1,319
CategoryTheory.Limits.IsColimitstatement and proof · cited by 773
CategoryTheory.Limits.WalkingSpanstatement · cited by 300
CategoryTheory.Limits.spanstatement · cited by 294
CategoryTheory.Limits.IsColimit.descproof · cited by 144
CategoryTheory.Limits.PushoutCoconestatement and proof · cited by 66
CategoryTheory.Limits.PushoutCocone.inlproof · cited by 58
CategoryTheory.Limits.PushoutCocone.inrproof · cited by 58

Cited by12

Results whose statement or proof uses this declaration.

CategoryTheory.Limits.pushoutSymmetryproof · cited by 30
CategoryTheory.IsPushout.flipproof · cited by 25
CategoryTheory.Limits.hasPushout_symmetryproof · cited by 18
CategoryTheory.Limits.inr_comp_pushoutSymmetry_homproof · cited by 5
CategoryTheory.Limits.inl_comp_pushoutSymmetry_homproof · cited by 4
CategoryTheory.Limits.pasteVertIsPushoutproof · cited by 4
CategoryTheory.Limits.PushoutCocone.isColimitOfFlipproof · cited by 1
CategoryTheory.Limits.preservesPushout_symmetryproof · cited by 0
CategoryTheory.Limits.botSquareIsPushoutproof · cited by 0
CategoryTheory.epi_iff_isIso_inrproof · cited by 0
CategoryTheory.regularOfIsPushoutFstOfRegularproof · cited by 0
CategoryTheory.normalOfIsPushoutFstOfNormalproof · cited by 0