Theorems · Theorem · category theory
CategoryTheory.IsPushout.isVanKampen_iff
∀ {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}
(H : CategoryTheory.IsPushout f g h i),
H.IsVanKampen ↔ CategoryTheory.IsVanKampenColimit (CategoryTheory.Limits.PushoutCocone.mk h i ⋯)- Defined in
- Mathlib.CategoryTheory.Adhesive.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 36 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites55
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.Functor.objproof · cited by 19,642
- CategoryTheory.CategoryStruct.compproof · cited by 17,999
- CategoryTheory.Functorproof · cited by 16,252
- CategoryTheory.Functor.mapproof · cited by 8,698
- CategoryTheory.NatTrans.appproof · cited by 7,406
- CategoryTheory.Category.assocproof · cited by 6,433
- CategoryTheory.CategoryStruct.idproof · cited by 6,235
- CategoryTheory.Category.comp_idproof · cited by 2,119
- CategoryTheory.Category.id_compproof · cited by 1,998
- CategoryTheory.Limits.Cocone.ptproof · cited by 1,354
Cited by2
Results whose statement or proof uses this declaration.
- CategoryTheory.adhesive_of_preserves_and_reflectsproof · cited by 1
- CategoryTheory.adhesive_of_reflectiveproof · cited by 0