Theorems · Theorem · commutative algebra

Module.DirectLimit.of_f

∀ {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] {i j : ι} {hij : i ≤ j} {x : G i},
  (Module.DirectLimit.of R ι G f j) ((f i j hij) x) = (Module.DirectLimit.of R ι G f i) x

Defined in

Mathlib.Algebra.Colimit.Module

Cited by

3 results in Mathlib

Foundations

Depth 50 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringPreorderAddCommMonoidModuleDecidableEq