Theorems · Theorem · category theory
CategoryTheory.Subobject.map_obj_injective
∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {X Y : C} (f : X ⟶ Y) [inst_1 : CategoryTheory.Mono f],
Function.Injective (CategoryTheory.Subobject.map f).obj- Defined in
- Mathlib.CategoryTheory.Subobject.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 45 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
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 and proof · cited by 19,642
- CategoryTheory.CategoryStruct.compproof · cited by 17,999
- CategoryTheory.Category.assocproof · cited by 6,433
- CategoryTheory.Monostatement and proof · cited by 893
- CategoryTheory.cancel_monoproof · cited by 435
- CategoryTheory.Subobjectstatement and proof · cited by 385
- CategoryTheory.Subobject.mkproof · cited by 109
- CategoryTheory.Subobject.mapstatement and proof · cited by 19
- CategoryTheory.Subobject.ofMkLEMkproof · cited by 18
- CategoryTheory.Subobject.mk_eq_mk_of_commproof · cited by 10
Cited by3
Results whose statement or proof uses this declaration.
- CategoryTheory.isNoetherianObject_of_monoproof · cited by 0
- CategoryTheory.Subobject.hasCardinalLT_of_monoproof · cited by 0
- CategoryTheory.isArtinianObject_of_monoproof · cited by 0