Theorems · Theorem · category theory
CategoryTheory.Subobject.nontrivial_of_not_isZero
∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] [CategoryTheory.Limits.HasZeroMorphisms C]
[CategoryTheory.Limits.HasZeroObject C] {X : C},
¬CategoryTheory.Limits.IsZero X → Nontrivial (CategoryTheory.Subobject X)A nonzero object has nontrivial subobject lattice.
- Defined in
- Mathlib.CategoryTheory.Subobject.Lattice
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 44 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- CategoryTheory.CategoryStruct.idproof · cited by 6,235
- CategoryTheory.Limits.HasZeroMorphismsstatement and proof · cited by 3,275
- Nontrivialstatement · cited by 2,416
- CategoryTheory.Limits.HasZeroObjectstatement and proof · cited by 1,298
- CategoryTheory.Iso.symmproof · cited by 993
- CategoryTheory.Subobjectstatement · cited by 385
- CategoryTheory.Limits.IsZerostatement and proof · cited by 306
- CategoryTheory.Subobject.mkproof · cited by 109
- CategoryTheory.Limits.IsZero.of_isoproof · cited by 35
- CategoryTheory.Limits.isZero_zeroproof · cited by 34
- CategoryTheory.Subobject.isoOfMkEqMkproof · cited by 7
Cited by1
Results whose statement or proof uses this declaration.
- CategoryTheory.exists_simple_subobjectproof · cited by 0