Theorems · Theorem · commutative algebra

Module.DirectLimit.linearEquiv_of

∀ {R : Type u_1} [inst : Semiring R] {ι : Type u_2} [inst_1 : Preorder ι] (G : ι → Type u_3)
  [inst_2 : (i : ι) → AddCommMonoid (G i)] [inst_3 : (i : ι) → Module R (G i)] (f : (i j : ι) → i ≤ j → G i →ₗ[R] G j)
  [inst_4 : DecidableEq ι] [inst_5 : Nonempty ι] [inst_6 : IsDirectedOrder ι]
  [inst_7 : DirectedSystem G fun x1 x2 x3 => ⇑(f x1 x2 x3)] {i : ι} {g : G i},
  (Module.DirectLimit.linearEquiv G f) ((Module.DirectLimit.of R ι G f i) g) = ⟦⟨i, g⟩⟧

Defined in

Mathlib.Algebra.Colimit.Module

Cited by

1 results in Mathlib

Foundations

Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringPreorderAddCommMonoidModuleDecidableEqNonemptyIsDirectedOrderDirectedSystem