Theorems · Theorem · category theory
ModuleCat.directLimitCocone_pt_carrier
∀ {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)], ↑(ModuleCat.directLimitCocone G f).pt = Module.DirectLimit G f- Cited by
- 0 results in Mathlib
- Foundations
- Depth 53 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement and proof · cited by 18,349
- AddCommGroupstatement and proof · cited by 12,871
- LinearMapstatement and proof · cited by 10,215
- Preorderstatement and proof · cited by 7,952
- Ringstatement and proof · cited by 7,463
- ModuleCatstatement · cited by 1,429
- CategoryTheory.Limits.Cocone.ptstatement and proof · cited by 1,354
- ModuleCat.carrierstatement and proof · cited by 997
- DirectedSystemstatement and proof · cited by 174
- Module.DirectLimitstatement · cited by 41
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