Theorems · Theorem · category theory
CategoryTheory.IsPushout.IsVanKampen.isPullback_of_mono_left
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {W X Y Z : C} {f : W ⟶ X} {g : W ⟶ Y} {h : X ⟶ Z} {i : Y ⟶ Z}
[CategoryTheory.Mono f] {H : CategoryTheory.IsPushout f g h i}, H.IsVanKampen → CategoryTheory.IsPullback f g h i- Defined in
- Mathlib.CategoryTheory.Adhesive.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 37 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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.idproof · cited by 6,235
- CategoryTheory.Category.comp_idproof · cited by 2,119
- CategoryTheory.Category.id_compproof · cited by 1,998
- CategoryTheory.Monostatement and proof · cited by 893
- CategoryTheory.IsPullbackstatement · cited by 320
- CategoryTheory.IsPushoutstatement and proof · cited by 219
- CategoryTheory.IsPullback.flipproof · cited by 61
- CategoryTheory.IsPushout.toCommSqproof · cited by 35
- CategoryTheory.IsPullback.of_vert_isIsoproof · cited by 21
- CategoryTheory.IsPushout.IsVanKampenstatement and proof · cited by 13
Cited by1
Results whose statement or proof uses this declaration.
- CategoryTheory.Adhesive.isPullback_of_isPushout_of_mono_leftproof · cited by 0