Theorems · Definition · category theory
ModuleCat.subobjectModule
{R : Type u} → [inst : Ring R] → (M : ModuleCat R) → CategoryTheory.Subobject M ≃o Submodule R ↑MThe categorical subobjects of a module M are in one-to-one correspondence with its
submodules.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Ring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Ringstatement and proof · cited by 7,463
- Submodulestatement and proof · cited by 7,192
- ModuleCatstatement and proof · cited by 1,429
- ModuleCat.carrierstatement and proof · cited by 997
- LinearMap.rangeproof · cited by 893
- OrderIsostatement · cited by 874
- Submodule.subtypeproof · cited by 480
- OrderIso.symmproof · cited by 475
- CategoryTheory.Subobjectstatement and proof · cited by 385
- ModuleCat.Hom.homproof · cited by 341
- ModuleCat.ofHomproof · cited by 200
- CategoryTheory.Subobject.arrowproof · cited by 175
Cited by1
Results whose statement or proof uses this declaration.
- simple_iff_isSimpleModuleproof · cited by 1