Theorems · Definition · category theory
ModuleCat.monoidAlgebraFree
(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 monoid algebra R[X].
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 83 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
- CategoryTheory.ConcreteCategory.homproof · cited by 4,022
- ModuleCatstatement · cited by 1,429
- ModuleCat.ofproof · cited by 594
- MonoidAlgebraproof · cited by 590
- ModuleCat.ofHomproof · cited by 200
- MonoidAlgebra.mapDomainLinearMapproof · cited by 17
Cited by5
Results whose statement or proof uses this declaration.
- Rep.standardComplex.forget₂ToModuleCatHomotopyEquiv_f_0_eqproof · cited by 2
- ModuleCat.monoidAlgebraFree_obj_carrierstatement and proof · cited by 0
- classifyingSpaceUniversalCover.compForgetAugmented.toModuleproof · cited by 0
- ModuleCat.monoidAlgebraFree_mapstatement and proof · cited by 0