Theorems · Definition · category theory
ModuleCat.free
(R : Type u) → [inst : Ring R] → CategoryTheory.Functor (Type u) (ModuleCat R)
The free functor Type u ⥤ ModuleCat R sending a type X to the
free R-module with generators x : X, implemented as the type X →₀ R.
- Cited by
- 19 results in Mathlib
- Foundations
- Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Ring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Quiver.Homproof · cited by 32,603
- CategoryTheory.Functorstatement · cited by 16,252
- Ringstatement and proof · cited by 7,463
- Finsuppproof · cited by 5,255
- CategoryTheory.ConcreteCategory.homproof · cited by 4,022
- ModuleCatstatement · cited by 1,429
- ModuleCat.ofproof · cited by 594
- ModuleCat.ofHomproof · cited by 200
- Finsupp.lmapDomainproof · cited by 63
Cited by31
Results whose statement or proof uses this declaration.
- ModuleCat.freeMkstatement · cited by 18
- LightCondensed.freeproof · cited by 12
- PresheafOfModules.freeproof · cited by 8
- PresheafOfModules.freeObjproof · cited by 7
- ModuleCat.freeDescstatement · cited by 4
- ModuleCat.freeHomEquivstatement and proof · cited by 3
- ModuleCat.FreeMonoidal.μIsostatement · cited by 2
- ModuleCat.FreeMonoidal.εIsostatement · cited by 2
- ModuleCat.adjstatement · cited by 1
- ModuleCat.FreeMonoidal.εIso_inv_freeMkstatement · cited by 1
- ModuleCat.FreeMonoidal.μIso_hom_freeMk_tmul_freeMkstatement · cited by 1
- ModuleCat.FreeMonoidal.μIso_inv_freeMkstatement · cited by 1