Theorems · Theorem · commutative algebra

Submodule.FG.lTensor.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 }] (Q : { Q // Q.FG })
  (u : TensorProduct R M ↥↑Q),
  (Submodule.FG.lTensor.directLimit R M N)
      ((Module.DirectLimit.of R { Q // Q.FG } (fun Q => TensorProduct R M ↥↑Q)
          (fun x x_1 hPQ => LinearMap.lTensor M (Submodule.inclusion hPQ)) Q)
        u) =
    (LinearMap.lTensor M (↑Q).subtype) u

Defined in

Mathlib.RingTheory.TensorProduct.DirectLimitFG

Cited by

1 results in Mathlib

Foundations

Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringAddCommMonoidModuleAddCommMonoidModuleDecidableEq