Theorems · Theorem · commutative algebra
ModuleCat.injectiveDimension_le_injectiveDimension_of_isLocalizedModule
∀ {R : Type u} [inst : CommRing R] [inst_1 : Small.{v, u} R] [IsNoetherianRing R] (S : Submonoid R) (M : ModuleCat R),
CategoryTheory.injectiveDimension (M.localizedModule S) ≤ CategoryTheory.injectiveDimension M- Cited by
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- Foundations
- Depth 123 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites21
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- ENatstatement and proof · cited by 4,985
- Submonoidstatement and proof · cited by 3,086
- WithBotstatement and proof · cited by 1,498
- ModuleCatstatement and proof · cited by 1,429
- ModuleCat.carrierproof · cited by 997
- ModuleCat.ofproof · cited by 594
- Smallstatement and proof · cited by 369
- Localizationstatement and proof · cited by 270
- IsNoetherianRingstatement and proof · cited by 268
- LocalizedModuleproof · cited by 154
- Shrinkproof · cited by 132
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