Theorems · Definition · category theory

ModuleCat.directLimitDiagram

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

The diagram (in the sense of CategoryTheory) of an unbundled directLimit of modules.

Defined in

Mathlib.Algebra.Category.ModuleCat.Limits

Cited by

5 results in Mathlib

Foundations

Depth 31 from the axioms · uses propext, Quot.sound

Assumes

RingPreorderAddCommGroupModuleDirectedSystem