Theorems · Definition · category theory
CategoryTheory.Functor.FullyFaithful.preimage
{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.FullyFaithful → {X Y : C} → (F.obj X ⟶ F.obj Y) → (X ⟶ Y)The inverse map (F.obj X ⟶ F.obj Y) ⟶ (X ⟶ Y) of F.map.
- Cited by
- 64 results in Mathlib
- Foundations
- Depth 3 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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.FullyFaithfulstatement and proof · cited by 87
Cited by101
Results whose statement or proof uses this declaration.
- CategoryTheory.Functor.FullyFaithful.map_preimagestatement · cited by 33
- CategoryTheory.Functor.FullyFaithful.homEquivproof · cited by 31
- CategoryTheory.Adjunction.Triple.rightToLeftproof · cited by 19
- AlgebraicGeometry.tilde.mapproof · cited by 11
- CategoryTheory.Functor.FullyFaithful.preimageIsoproof · cited by 10
- CategoryTheory.SimplicialObject.Splitting.toNondegComplexproof · cited by 9
- AlgebraicGeometry.Scheme.Modules.fromTildeΓproof · cited by 9
- CategoryTheory.SimplicialObject.Splitting.fromNondegComplexproof · cited by 7
- CategoryTheory.Functor.FullyFaithful.whiskeringRightproof · cited by 6
- CategoryTheory.Functor.FullyFaithful.addGrpObjproof · cited by 4
- CategoryTheory.Functor.FullyFaithful.grpObjproof · cited by 4
- CategoryTheory.Functor.FullyFaithful.homEquiv_symm_applystatement · cited by 4