Theorems · Theorem · category theory
CategoryTheory.IsVanKampenColimit.of_iso
∀ {J : Type v'} [inst : CategoryTheory.Category.{u', v'} J] {C : Type u} [inst_1 : CategoryTheory.Category.{v, u} C]
{F : CategoryTheory.Functor J C} {c c' : CategoryTheory.Limits.Cocone F},
CategoryTheory.IsVanKampenColimit c → ∀ (e : c ≅ c'), CategoryTheory.IsVanKampenColimit c'- Defined in
- Mathlib.CategoryTheory.Limits.VanKampen
- Cited by
- 9 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.
Cites29
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.Homproof · cited by 32,603
- CategoryTheory.Functor.objproof · cited by 19,642
- CategoryTheory.CategoryStruct.compproof · cited by 17,999
- CategoryTheory.Functorstatement and proof · cited by 16,252
- CategoryTheory.Functor.mapproof · cited by 8,698
- CategoryTheory.NatTrans.appproof · cited by 7,406
- CategoryTheory.Iso.invproof · cited by 6,514
- CategoryTheory.Category.assocproof · cited by 6,433
- CategoryTheory.CategoryStruct.idproof · cited by 6,235
- CategoryTheory.Isostatement and proof · cited by 3,963
- CategoryTheory.Category.comp_idproof · cited by 2,119
Cited by9
Results whose statement or proof uses this declaration.
- CategoryTheory.IsVanKampenColimit.precompose_isIso_iffproof · cited by 4
- CategoryTheory.finitaryExtensive_of_preserves_and_reflectsproof · cited by 2
- CategoryTheory.IsVanKampenColimit.whiskerEquivalence_iffproof · cited by 2
- CategoryTheory.isVanKampenColimit_of_isEmptyproof · cited by 2
- CategoryTheory.FinitaryExtensive.isVanKampen_finiteCoproducts_Finproof · cited by 1
- CategoryTheory.adhesive_of_preserves_and_reflectsproof · cited by 1
- CategoryTheory.IsVanKampenColimit.mapCocone_iffproof · cited by 0
- CategoryTheory.finitaryExtensive_of_reflectiveproof · cited by 0
- CategoryTheory.adhesive_of_reflectiveproof · cited by 0