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Theorems · Theorem · category theory

CategoryTheory.Limits.hasPushout_symmetry

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

Making this a global instance would make the typeclass search go in an infinite loop.

Defined in
Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback
Cited by
18 results in Mathlib
Foundations
Depth 31 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.Limits.HasPushout

Around this declaration

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

CategoryTheory.Limits.pushoutSymmetry · cited by 30Limits.pushoutSymmetryCategoryTheory.Limits.inl_comp_pushoutSymmetry_hom_assoc · cited by 8Limits.inl_comp_pushoutSy…CategoryTheory.Limits.inr_comp_pushoutSymmetry_hom_assoc · cited by 7Limits.inr_comp_pushoutSy…CategoryTheory.Limits.inr_comp_pushoutSymmetry_hom · cited by 5Limits.inr_comp_pushoutSy…CategoryTheory.Limits.inl_comp_pushoutSymmetry_hom · cited by 4Limits.inl_comp_pushoutSy…CategoryTheory.MonoidalCategory.Limits.whiskerLeft_inl_comp_pushoutSymmetry_hom_assoc · cited by 3Limits.whiskerLeft_inl_co…CategoryTheory.MonoidalCategory.Limits.inl_comp_pushoutSymmetry_hom_whiskerRight_assoc · cited by 2Limits.inl_comp_pushoutSy…CategoryTheory.MonoidalCategory.Limits.inr_comp_pushoutSymmetry_hom_whiskerRight_assoc · cited by 2Limits.inr_comp_pushoutSy…CategoryTheory.MonoidalCategory.Limits.whiskerLeft_inr_comp_pushoutSymmetry_hom_assoc · cited by 2Limits.whiskerLeft_inr_co…CategoryTheory.Limits.hasPushouts_symmetry_of_hasPushoutsAlong · cited by 1Limits.hasPushouts_symmet…CategoryTheory.Limits.inl_comp_pushoutSymmetry_inv · cited by 1Limits.inl_comp_pushoutSy…CategoryTheory.MonoidalCategory.Limits.inl_comp_pushoutSymmetry_hom_whiskerRight · cited by 1Limits.inl_comp_pushoutSy…CategoryTheory.MonoidalCategory.Limits.inr_comp_pushoutSymmetry_hom_whiskerRight · cited by 1Limits.inr_comp_pushoutSy…CategoryTheory.MonoidalCategory.Limits.whiskerLeft_inl_comp_pushoutSymmetry_hom · cited by 1Limits.whiskerLeft_inl_co…CategoryTheory.MonoidalCategory.Limits.whiskerLeft_inr_comp_pushoutSymmetry_hom · cited by 1Limits.whiskerLeft_inr_co…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.Limits.pushout.inr · cited by 193pushout.inrCategoryTheory.Limits.HasPushout · cited by 192Limits.HasPushoutCategoryTheory.Limits.pushout.inl · cited by 192pushout.inlCategoryTheory.Limits.PushoutCocone.mk · cited by 89PushoutCocone.mkCategoryTheory.Limits.pushout.condition · cited by 23pushout.conditionCategoryTheory.Limits.pushoutIsPushout · cited by 7Limits.pushoutIsPushoutCategoryTheory.Limits.PushoutCocone.flipIsColimit · cited by 6PushoutCocone.flipIsColim…CategoryTheory.Limits.PushoutCocone.flip · cited by 4PushoutCocone.flipLimits.hasPushout_symmetryCITED BYCITES

Cites10

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by19

Results whose statement or proof uses this declaration.