Theorems · Theorem · category theory
CategoryTheory.Functor.FullyFaithful.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} (hF : F.FullyFaithful) (X Y : C), Function.Bijective F.map- Cited by
- 2 results in Mathlib
- Foundations
- Depth 15 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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 · cited by 32,603
- CategoryTheory.Functor.objstatement · cited by 19,642
- CategoryTheory.Functorstatement and proof · cited by 16,252
- CategoryTheory.Functor.mapstatement · cited by 8,698
- Function.Bijectivestatement · cited by 863
- Equiv.bijectiveproof · cited by 132
- CategoryTheory.Functor.FullyFaithfulstatement and proof · cited by 87
- CategoryTheory.Functor.FullyFaithful.homEquivproof · cited by 31
Cited by2
Results whose statement or proof uses this declaration.
- CategoryTheory.Functor.FullyFaithful.nonempty_iff_map_bijectiveproof · cited by 1
- DerivedCategory.Plus.Qh_map_bijective_of_isKInjectiveproof · cited by 0