Theorems · Theorem · category theory
CategoryTheory.isSeparator_iff_faithful_coyoneda_obj
∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] (G : C),
CategoryTheory.IsSeparator G ↔ (CategoryTheory.coyoneda.obj (Opposite.op G)).Faithful- Defined in
- Mathlib.CategoryTheory.Generator.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 28 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
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
- Quiver.Homproof · cited by 32,603
- CategoryTheory.Functor.objstatement and proof · cited by 19,642
- CategoryTheory.CategoryStruct.compproof · cited by 17,999
- CategoryTheory.Functorstatement · cited by 16,252
- CategoryTheory.Functor.mapproof · cited by 8,698
- Oppositestatement · cited by 8,081
- CategoryTheory.Functor.Faithfulstatement and proof · cited by 313
- CategoryTheory.coyonedastatement and proof · cited by 208
- CategoryTheory.ConcreteCategory.congr_homproof · cited by 138
- CategoryTheory.ConcreteCategory.extproof · cited by 107
- CategoryTheory.Functor.map_injectiveproof · cited by 91
Cited by1
Results whose statement or proof uses this declaration.
- CategoryTheory.isSeparator_iff_faithful_preadditiveCoyonedaproof · cited by 1