Theorems · Definition · category theory

ModuleCat.directLimitIsColimit

{R : Type u} →
  [inst : Ring R] →
    {ι : Type v} →
      [inst_1 : DecidableEq ι] →
        [inst_2 : Preorder ι] →
          (G : ι → Type v) →
            [inst_3 : (i : ι) → AddCommGroup (G i)] →
              [inst_4 : (i : ι) → Module R (G i)] →
                (f : (i j : ι) → i ≤ j → G i →ₗ[R] G j) →
                  [inst_5 : DirectedSystem G fun i j h => ⇑(f i j h)] →
                    CategoryTheory.Limits.IsColimit (ModuleCat.directLimitCocone G f)

The unbundled directLimit of modules is a colimit in the sense of CategoryTheory.

Defined in

Mathlib.Algebra.Category.ModuleCat.Limits

Cited by

1 results in Mathlib

Foundations

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

Assumes

RingDecidableEqPreorderAddCommGroupModuleDirectedSystem