Theorems · Theorem · category theory
Module.injective_iff_injective_object
∀ (R : Type u) (M : Type v) [inst : Ring R] [inst_1 : AddCommGroup M] [inst_2 : Module R M], Module.Injective R M ↔ CategoryTheory.Injective (ModuleCat.of R M)
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- RingAddCommGroupModule
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- Ringstatement and proof · cited by 7,463
- ModuleCatstatement · cited by 1,429
- ModuleCat.ofstatement and proof · cited by 594
- CategoryTheory.Injectivestatement and proof · cited by 70
- Module.Injectivestatement and proof · cited by 20
- Module.injective_module_of_injective_objectproof · cited by 2
- Module.injective_object_of_injective_moduleproof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- ModuleCat.hasInjectiveDimensionLE_iff_forall_maximalSpectrumproof · cited by 2
- ModuleCat.localizedModule_hasInjectiveDimensionLEproof · cited by 2