Theorems · Theorem · category theory
CommRingCat.FilteredColimits.nontrivial
∀ {J : Type v} [inst : CategoryTheory.SmallCategory J] {F : CategoryTheory.Functor J CommRingCat}
[CategoryTheory.IsFilteredOrEmpty J] [∀ (i : J), Nontrivial ↑(F.obj i)] {c : CategoryTheory.Limits.Cocone F}
(hc : CategoryTheory.Limits.IsColimit c), Nontrivial ↑c.pt- Cited by
- 0 results in Mathlib
- Foundations
- Depth 56 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites31
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Quiver.Homproof · cited by 32,603
- CategoryTheory.Functor.objstatement and proof · cited by 19,642
- CategoryTheory.Functorstatement and proof · cited by 16,252
- CategoryTheory.Functor.mapproof · cited by 8,698
- CategoryTheory.NatTrans.appproof · cited by 7,406
- CategoryTheory.Functor.compproof · cited by 6,529
- CategoryTheory.ConcreteCategory.homproof · cited by 4,022
- Nontrivialstatement and proof · cited by 2,416
- CommRingCatstatement and proof · cited by 2,333
- CategoryTheory.Limits.Cocone.ptstatement · cited by 1,354
- CommRingCat.carrierstatement and proof · cited by 1,096
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.