Theorems · Theorem · category theory
CategoryTheory.CommSq.flip
∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] {W X Y Z : C} {f : W ⟶ X} {g : W ⟶ Y} {h : X ⟶ Z}
{i : Y ⟶ Z}, CategoryTheory.CommSq f g h i → CategoryTheory.CommSq g f i h- Defined in
- Mathlib.CategoryTheory.CommSq
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 10 from the axioms · uses no axioms
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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.CommSqstatement and proof · cited by 158
- CategoryTheory.CommSq.wproof · cited by 122
Cited by15
Results whose statement or proof uses this declaration.
- CategoryTheory.CommSq.horiz_invproof · cited by 10
- CategoryTheory.IsPushout.opproof · cited by 7
- CategoryTheory.IsPullback.unopproof · cited by 6
- CategoryTheory.IsPullback.opproof · cited by 5
- CategoryTheory.IsPushout.unopproof · cited by 4
- CategoryTheory.IsPullback.of_vert_isIso_monoproof · cited by 2
- CategoryTheory.CommSq.coconeOpstatement · cited by 1
- CategoryTheory.CommSq.coconeUnopstatement · cited by 1
- CategoryTheory.CommSq.coneOpstatement · cited by 1
- CategoryTheory.CommSq.coneUnopstatement · cited by 1
- CategoryTheory.IsPushout.IsVanKampen.flipproof · cited by 1
- CategoryTheory.IsPushout.IsVanKampen.isPullback_of_mono_leftproof · cited by 1