Theorems · Definition · category theory
CategoryTheory.IsSeparator
{C : Type u₁} → [CategoryTheory.Category.{v₁, u₁} C] → C → PropWe say that G is a separator if the functor C(G, -) is faithful.
- Defined in
- Mathlib.CategoryTheory.Generator.Basic
- Cited by
- 58 results in Mathlib
- Foundations
- Depth 4 from the axioms · uses no axioms
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
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.ObjectProperty.IsSeparatingproof · cited by 41
- CategoryTheory.ObjectProperty.singletonproof · cited by 20
Cited by65
Results whose statement or proof uses this declaration.
- CategoryTheory.IsGrothendieckAbelian.generatingMonomorphisms.largerSubobjectstatement and proof · cited by 10
- CategoryTheory.isSeparator_defstatement and proof · cited by 5
- CategoryTheory.IsSeparator.isDetectorstatement · cited by 4
- CategoryTheory.IsSeparator.defstatement · cited by 3
- CategoryTheory.IsGrothendieckAbelian.generatingMonomorphisms.largerSubobject_topstatement and proof · cited by 3
- CategoryTheory.isSeparator_separatorstatement · cited by 3
- CategoryTheory.ObjectProperty.IsSeparating.isSeparator_coproductstatement · cited by 3
- CategoryTheory.IsGrothendieckAbelian.GabrielPopescuAux.kernel_ι_d_comp_dstatement and proof · cited by 2
- CategoryTheory.IsGrothendieckAbelian.generatingMonomorphisms.exists_larger_subobjectstatement and proof · cited by 2
- CategoryTheory.IsGrothendieckAbelian.generatingMonomorphisms.functorToMonoOverstatement and proof · cited by 2
- CategoryTheory.IsGrothendieckAbelian.generatingMonomorphisms.lt_largerSubobjectstatement and proof · cited by 2
- CategoryTheory.isSeparator_coprodstatement · cited by 2