Theorems · Theorem · commutative algebra

Module.DirectLimit.lift.congr_simp

∀ (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] {P : Type u_4} [inst_5 : AddCommMonoid P] [inst_6 : Module R P]
  (g g_1 : (i : ι) → G i →ₗ[R] P) (e_g : g = g_1)
  (Hg : ∀ (i j : ι) (hij : i ≤ j) (x : G i), (g j) ((f i j hij) x) = (g i) x),
  Module.DirectLimit.lift R ι G f g Hg = Module.DirectLimit.lift R ι G f g_1 ⋯

Defined in

Mathlib.Algebra.Colimit.Module

Cited by

0 results in Mathlib

Foundations

Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringPreorderAddCommMonoidModuleDecidableEqAddCommMonoidModule