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Theorems · Definition · category theory

CategoryTheory.Limits.PushoutCocone.isColimitOfFlip

{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.flip → CategoryTheory.Limits.IsColimit t

A square is a pushout square if its flip is.

Defined in
Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackCone
Cited by
1 results in Mathlib
Foundations
Depth 34 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.Category
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

CategoryTheory.Limits.pasteVertIsPushout · cited by 4Limits.pasteVertIsPushoutCategoryTheory.Limits.preservesPushout_symmetry · cited by 0Limits.preservesPushout_s…CategoryTheory.Limits.botSquareIsPushout · cited by 0Limits.botSquareIsPushoutCategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.Limits.WalkingPair · cited by 1319Limits.WalkingPairCategoryTheory.Limits.IsColimit · cited by 773Limits.IsColimitCategoryTheory.Limits.WalkingSpan · cited by 300Limits.WalkingSpanCategoryTheory.Limits.span · cited by 294Limits.spanCategoryTheory.Limits.PushoutCocone · cited by 66Limits.PushoutCoconeCategoryTheory.Limits.IsColimit.ofIsoColimit · cited by 45IsColimit.ofIsoColimitCategoryTheory.Limits.PushoutCocone.flipIsColimit · cited by 6PushoutCocone.flipIsColim…CategoryTheory.Limits.PushoutCocone.flip · cited by 4PushoutCocone.flipCategoryTheory.Limits.PushoutCocone.flipFlipIso · cited by 0PushoutCocone.flipFlipIsoPushoutCocone.isColimitOfFlipCITED BYCITES

Cites11

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Cited by3

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