Theorems · Theorem · category theory
CategoryTheory.Functor.FullyFaithful.nonempty_iff_map_bijective
∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
(F : CategoryTheory.Functor C D), Nonempty F.FullyFaithful ↔ ∀ (X Y : C), Function.Bijective F.map- Cited by
- 1 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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.Homstatement and proof · cited by 32,603
- CategoryTheory.Functor.objstatement · cited by 19,642
- CategoryTheory.Functorstatement and proof · cited by 16,252
- CategoryTheory.Functor.mapstatement and proof · cited by 8,698
- Function.Bijectivestatement and proof · cited by 863
- CategoryTheory.Functor.Fullproof · cited by 341
- CategoryTheory.Functor.Faithfulproof · cited by 313
- Function.Bijective.injectiveproof · cited by 115
- Function.Bijective.surjectiveproof · cited by 114
- CategoryTheory.Functor.FullyFaithfulstatement and proof · cited by 87
- CategoryTheory.Functor.FullyFaithful.ofFullyFaithfulproof · cited by 21
Cited by1
Results whose statement or proof uses this declaration.
- CategoryTheory.Pseudofunctor.isPrestackFor_iff_isSheafForproof · cited by 1