Theorems · Theorem · category theory
PresheafOfModules.mono_of_injective
∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {R : CategoryTheory.Functor Cᵒᵖ RingCat}
{M₁ M₂ : PresheafOfModules R} {f : M₁ ⟶ M₂},
(∀ ⦃X : Cᵒᵖ⦄, Function.Injective ⇑(CategoryTheory.ConcreteCategory.hom (f.app X))) → CategoryTheory.Mono f- Cited by
- 1 results in Mathlib
- Foundations
- Depth 41 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites27
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- 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
- RingHom.idstatement · cited by 18,349
- CategoryTheory.CategoryStruct.compproof · cited by 17,999
- CategoryTheory.Functorstatement and proof · cited by 16,252
- LinearMapstatement · cited by 10,215
- Oppositestatement and proof · cited by 8,081
- CategoryTheory.Functor.compproof · cited by 6,529
- CategoryTheory.ConcreteCategory.homstatement and proof · cited by 4,022
- ModuleCatstatement and proof · cited by 1,429
Cited by1
Results whose statement or proof uses this declaration.
- PresheafOfModules.mono_iff_surjectiveproof · cited by 0