Theorems · Theorem · category theory

CategoryTheory.Functor.Faithful.of_comp

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
  {E : Type u₃} [inst_2 : CategoryTheory.Category.{v₃, u₃} E] (F : CategoryTheory.Functor C D)
  (G : CategoryTheory.Functor D E) [(F.comp G).Faithful], F.Faithful

Defined in: Mathlib.CategoryTheory.Functor.FullyFaithful
Cited by: 6 results in Mathlib
Foundations: Depth 16 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Category CategoryTheory.Category CategoryTheory.Functor.Faithful

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Cites6

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.Functorstatement and proof · cited by 16,252
CategoryTheory.Functor.compstatement and proof · cited by 6,529
CategoryTheory.Functor.Faithfulstatement and proof · cited by 313
CategoryTheory.Functor.map_injectiveproof · cited by 91
Function.Injective.of_compproof · cited by 82

Cited by6

Results whose statement or proof uses this declaration.

CategoryTheory.Functor.Faithful.of_comp_eqproof · cited by 1
CategoryTheory.Functor.Faithful.of_comp_isoproof · cited by 1
CategoryTheory.isSeparator_iff_faithful_preadditiveCoyonedaproof · cited by 1
CategoryTheory.isSeparator_iff_faithful_preadditiveCoyonedaObjproof · cited by 1
CategoryTheory.isCoseparator_iff_faithful_preadditiveYonedaproof · cited by 1
CategoryTheory.isCoseparator_iff_faithful_preadditiveYonedaObjproof · cited by 0