Theorems · Definition · category theory
CategoryTheory.IsCodetector
{C : Type u₁} → [CategoryTheory.Category.{v₁, u₁} C] → C → PropWe say that G is a codetector if the functor C(-, G) reflects isomorphisms.
- Defined in
- Mathlib.CategoryTheory.Generator.Basic
- Cited by
- 14 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.singletonproof · cited by 20
- CategoryTheory.ObjectProperty.IsCodetectingproof · cited by 13
Cited by16
Results whose statement or proof uses this declaration.
- CategoryTheory.isCodetector_defstatement and proof · cited by 2
- CategoryTheory.isCodetector_codetectorstatement · cited by 1
- CategoryTheory.isCodetector_coseparatorstatement · cited by 1
- CategoryTheory.isCodetector_op_iffstatement and proof · cited by 1
- CategoryTheory.isCodetector_unop_iffstatement and proof · cited by 1
- CategoryTheory.HasCodetector.hasCodetectorstatement · cited by 1
- CategoryTheory.IsCoseparator.isCodetectorstatement · cited by 1
- CategoryTheory.IsCodetector.defstatement · cited by 1
- CategoryTheory.IsCodetector.isCoseparatorstatement · cited by 1
- CategoryTheory.isDetector_op_iffstatement and proof · cited by 1
- CategoryTheory.isDetector_unop_iffstatement and proof · cited by 1
- CategoryTheory.isCodetector_iff_reflectsIsomorphisms_yoneda_objstatement and proof · cited by 0