Theorems · Inductive type · category theory
CategoryTheory.ObjectProperty.ContainsZero
{C : Type u} → [inst : CategoryTheory.Category.{v, u} C] → CategoryTheory.ObjectProperty C → PropGiven P : ObjectProperty C, we say that P.ContainsZero if there exists
a zero object for which P holds. When P is closed under isomorphisms,
this holds for any zero object.
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 2 from the axioms · uses no axioms
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement · cited by 32,673
- CategoryTheory.ObjectPropertystatement · cited by 798
Cited by18
Results whose statement or proof uses this declaration.
- CategoryTheory.ObjectProperty.exists_prop_of_containsZerostatement and proof · cited by 3
- CategoryTheory.ObjectProperty.prop_of_isZerostatement and proof · cited by 3
- CategoryTheory.ObjectProperty.monotone'_extensionProductIterstatement and proof · cited by 2
- CategoryTheory.ObjectProperty.le_extensionProductIterstatement and proof · cited by 1
- CategoryTheory.ObjectProperty.le_extensionProduct_rightstatement and proof · cited by 1
- CategoryTheory.ObjectProperty.ContainsZero.exists_zerostatement and proof · cited by 1
- CategoryTheory.ObjectProperty.prop_zerostatement and proof · cited by 0
- CategoryTheory.ObjectProperty.preservesMonomorphisms_ι_of_isNormalEpiCategorystatement and proof · cited by 0
- CategoryTheory.ObjectProperty.le_extensionProduct_leftstatement and proof · cited by 0
- CategoryTheory.ObjectProperty.trW_of_isIsostatement and proof · cited by 0
- CategoryTheory.ObjectProperty.IsTriangulated.casesOnstatement and proof · cited by 0
- CategoryTheory.ObjectProperty.IsTriangulated.recOnstatement and proof · cited by 0