Theorems · Theorem · commutative algebra

Module.FinitePresentation.linearEquivMap_apply

∀ {R : Type u_3} {M : Type u_4} {N : Type u_5} [inst : CommRing R] [inst_1 : AddCommGroup M] [inst_2 : Module R M]
  [inst_3 : AddCommGroup N] [inst_4 : Module R N] (S : Submonoid R) [inst_5 : Module.FinitePresentation R M]
  (f : M →ₗ[R] N),
  (Module.FinitePresentation.linearEquivMap S) ((LocalizedModule.mkLinearMap S (M →ₗ[R] N)) f) =
    (IsLocalizedModule.map S (LocalizedModule.mkLinearMap S M) (LocalizedModule.mkLinearMap S N)) f

Defined in: Mathlib.Algebra.Module.FinitePresentation
Cited by: 0 results in Mathlib
Foundations: Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing AddCommGroup Module AddCommGroup Module Module.FinitePresentation

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DFunLike.coestatement · cited by 62,936
Modulestatement and proof · cited by 20,661
RingHom.idstatement and proof · cited by 18,349
CommRingstatement and proof · cited by 17,173
AddCommGroupstatement and proof · cited by 12,871
LinearMapstatement and proof · cited by 10,215
LinearEquivstatement · cited by 3,317
Submonoidstatement and proof · cited by 3,086
LocalizedModulestatement · cited by 154
LocalizedModule.mkLinearMapstatement and proof · cited by 76
IsLocalizedModule.mapstatement and proof · cited by 60
Module.FinitePresentationstatement and proof · cited by 60

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