Theorems · Theorem · ring theory
Module.injective_iff_ulift_injective
∀ (R : Type u) [inst : Ring R] (M : Type v) [inst_1 : AddCommGroup M] [inst_2 : Module R M] [Small.{v, u} R],
Module.Injective R M ↔ Module.Injective R (ULift.{v', v} M)- Defined in
- Mathlib.Algebra.Module.Injective
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- RingAddCommGroupModuleSmall
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Cites7
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
- Smallstatement and proof · cited by 369
- Module.Injectivestatement · cited by 20
- Module.injective_of_ulift_injectiveproof · cited by 1
- Module.ulift_injective_of_injectiveproof · cited by 1
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