Theorems · Theorem · ring theory

IsSimpleModule.obj_of_isEquivalence

∀ {R : Type u_3} {S : Type u_4} [inst : Ring R] [inst_1 : Ring S]
  (e : CategoryTheory.Functor (ModuleCat R) (ModuleCat S)) [e.IsEquivalence] (M : ModuleCat R) [IsSimpleModule R ↑M],
  IsSimpleModule S ↑(e.obj M)

Defined in: Mathlib.RingTheory.SimpleRing.DivisionRing
Cited by: 0 results in Mathlib
Foundations: Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Ring Ring CategoryTheory.Functor.IsEquivalence IsSimpleModule

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CategoryTheory.Functor.objstatement and proof · cited by 19,642
CategoryTheory.Functorstatement and proof · cited by 16,252
Ringstatement and proof · cited by 7,463
ModuleCatstatement and proof · cited by 1,429
ModuleCat.carrierstatement and proof · cited by 997
IsSimpleModulestatement and proof · cited by 114
CategoryTheory.Functor.IsEquivalencestatement and proof · cited by 111
CategoryTheory.simple_objproof · cited by 2
simple_iff_isSimpleModule'proof · cited by 2

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