Theorems · Definition · category theory
CategoryTheory.Subobject.map
{C : Type u₁} →
[inst : CategoryTheory.Category.{v₁, u₁} C] →
{X Y : C} →
(f : X ⟶ Y) →
[CategoryTheory.Mono f] → CategoryTheory.Functor (CategoryTheory.Subobject X) (CategoryTheory.Subobject Y)We can map subobjects of X to subobjects of Y
by post-composition with a monomorphism f : X ⟶ Y.
- Defined in
- Mathlib.CategoryTheory.Subobject.Basic
- Cited by
- 19 results in Mathlib
- Foundations
- Depth 35 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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.Functorstatement · cited by 16,252
- CategoryTheory.Monostatement and proof · cited by 893
- CategoryTheory.Subobjectstatement · cited by 385
- CategoryTheory.MonoOver.mapproof · cited by 12
- CategoryTheory.Subobject.lowerproof · cited by 6
Cited by21
Results whose statement or proof uses this declaration.
- CategoryTheory.Subobject.inf_eq_map_pullback'statement · cited by 3
- CategoryTheory.Subobject.map_obj_injectivestatement and proof · cited by 3
- CategoryTheory.Subobject.mapIsoToOrderIsoproof · cited by 2
- CategoryTheory.Subobject.pullback_map_selfstatement · cited by 1
- CategoryTheory.Subobject.map_compstatement · cited by 1
- CategoryTheory.Subobject.map_pullbackstatement · cited by 1
- CategoryTheory.isNoetherianObject_of_monoproof · cited by 0
- CategoryTheory.Subobject.hasCardinalLT_of_monoproof · cited by 0
- CategoryTheory.Subobject.map.congr_simpstatement and proof · cited by 0
- CategoryTheory.Subobject.mapIsoToOrderIso_applystatement · cited by 0
- CategoryTheory.Subobject.mapIsoToOrderIso_symm_applystatement · cited by 0
- CategoryTheory.Subobject.mapPullbackAdjstatement · cited by 0