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 fMaking this a global instance would make the typeclass search go in an infinite loop.
- Cited by
- 18 results in Mathlib
- Foundations
- Depth 31 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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.Limits.pushout.inrproof · cited by 193
- CategoryTheory.Limits.HasPushoutstatement and proof · cited by 192
- CategoryTheory.Limits.pushout.inlproof · cited by 192
- CategoryTheory.Limits.PushoutCocone.mkproof · cited by 89
- CategoryTheory.Limits.pushout.conditionproof · cited by 23
- CategoryTheory.Limits.pushoutIsPushoutproof · cited by 7
- CategoryTheory.Limits.PushoutCocone.flipIsColimitproof · cited by 6
- CategoryTheory.Limits.PushoutCocone.flipproof · cited by 4
Cited by19
Results whose statement or proof uses this declaration.
- CategoryTheory.Limits.pushoutSymmetrystatement · cited by 30
- CategoryTheory.Limits.inl_comp_pushoutSymmetry_hom_assocstatement · cited by 8
- CategoryTheory.Limits.inr_comp_pushoutSymmetry_hom_assocstatement · 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 · cited by 3
- CategoryTheory.MonoidalCategory.Limits.inl_comp_pushoutSymmetry_hom_whiskerRight_assocstatement · cited by 2
- CategoryTheory.MonoidalCategory.Limits.inr_comp_pushoutSymmetry_hom_whiskerRight_assocstatement · cited by 2
- CategoryTheory.MonoidalCategory.Limits.whiskerLeft_inr_comp_pushoutSymmetry_hom_assocstatement · cited by 2
- CategoryTheory.Limits.hasPushouts_symmetry_of_hasPushoutsAlongproof · cited by 1
- CategoryTheory.Limits.inl_comp_pushoutSymmetry_invstatement · cited by 1
- CategoryTheory.MonoidalCategory.Limits.inl_comp_pushoutSymmetry_hom_whiskerRightstatement · cited by 1