Theorems · Theorem · commutative algebra

Submodule.FG.rTensor.directLimit_apply

∀ (R : Type u) (M : Type u_1) (N : Type u_2) [inst : CommSemiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]
  [inst_3 : AddCommMonoid N] [inst_4 : Module R N] [inst_5 : DecidableEq { P // P.FG }] {P : { P // P.FG }}
  (u : TensorProduct R (↥↑P) N),
  (Submodule.FG.rTensor.directLimit R M N)
      ((Module.DirectLimit.of R { P // P.FG } (fun P => TensorProduct R (↥↑P) N)
          (fun ⦃x x_1⦄ h => LinearMap.rTensor N (Submodule.inclusion h)) P)
        u) =
    (LinearMap.rTensor N (↑P).subtype) u

Defined in

Mathlib.RingTheory.TensorProduct.DirectLimitFG

Cited by

2 results in Mathlib

Foundations

Depth 98 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringAddCommMonoidModuleAddCommMonoidModuleDecidableEq