Theorems · Inductive type · category theory
CategoryTheory.ObjectProperty.Nonempty
{C : Type u} → [inst : CategoryTheory.CategoryStruct.{v, u} C] → CategoryTheory.ObjectProperty C → PropNonempty P is a typeclass saying there exists an object X : C that satisfies P.
- Cited by
- 13 results in Mathlib
- Foundations
- Depth 2 from the axioms · uses no axioms
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.ObjectPropertystatement · cited by 798
- CategoryTheory.CategoryStructstatement · cited by 343
Cited by16
Results whose statement or proof uses this declaration.
- CategoryTheory.ObjectProperty.nonempty_of_propstatement · cited by 5
- CategoryTheory.ObjectProperty.arbitrarystatement and proof · cited by 3
- CategoryTheory.ObjectProperty.prop_arbitrarystatement and proof · cited by 2
- CategoryTheory.ObjectProperty.monotone'_triangEnvelopeIterproof · cited by 1
- CategoryTheory.ObjectProperty.exists_prop_of_nonemptystatement and proof · cited by 1
- CategoryTheory.ObjectProperty.nonempty_iffstatement and proof · cited by 1
- CategoryTheory.ObjectProperty.nonempty_iff_ne_botstatement and proof · cited by 1
- CategoryTheory.ObjectProperty.Nonempty.casesOnstatement and proof · cited by 1
- CategoryTheory.ObjectProperty.Nonempty.exists_propstatement and proof · cited by 1
- CategoryTheory.MorphismProperty.nonempty_cokernelsstatement · cited by 0
- CategoryTheory.MorphismProperty.nonempty_kernelsstatement · cited by 0
- CategoryTheory.ObjectProperty.nonempty_iSupstatement and proof · cited by 0