Theorems · Definition · category theory
CategoryTheory.Functor.FullyFaithful.ofFullyFaithful
{C : Type u₁} →
[inst : CategoryTheory.Category.{v₁, u₁} C] →
{D : Type u₂} →
[inst_1 : CategoryTheory.Category.{v₂, u₂} D] →
(F : CategoryTheory.Functor C D) → [F.Full] → [F.Faithful] → F.FullyFaithfulA FullyFaithful structure can be obtained from the assumption the F is both
full and faithful.
- Cited by
- 21 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses propext, Classical.choice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
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.Fullstatement and proof · cited by 341
- CategoryTheory.Functor.Faithfulstatement and proof · cited by 313
- CategoryTheory.Functor.FullyFaithfulstatement · cited by 87
- CategoryTheory.Functor.preimageproof · cited by 55
Cited by34
Results whose statement or proof uses this declaration.
- CategoryTheory.Adjunction.Triple.rightToLeftproof · cited by 19
- CategoryTheory.Abelian.Ext.mk₀_bijectiveproof · cited by 3
- CategoryTheory.ObjectProperty.isLocal_adj_unit_appproof · cited by 3
- CategoryTheory.Adjunction.Triple.rightToLeft_eq_counitsproof · cited by 2
- CategoryTheory.unitCompPartialBijectiveAuxproof · cited by 2
- CategoryTheory.Adjunction.Triple.whiskerRight_rightToLeftproof · cited by 2
- CategoryTheory.Pseudofunctor.IsStackFor.isPrestackForproof · cited by 2
- CategoryTheory.PreGaloisCategory.endEquivSectionsFibersproof · cited by 2
- CategoryTheory.Adjunction.Triple.rightToLeft_eq_unitsproof · cited by 1
- CategoryTheory.unitCompPartialBijectiveAux_symm_applyproof · cited by 1
- CategoryTheory.Adjunction.isIso_map_unit_of_isLeftAdjoint_compproof · cited by 1
- CategoryTheory.SingleFunctors.lift.shiftIsoproof · cited by 1