monoid ring functor
- notation: : →
- Source: category of monoids
- Target: category of rings
- Right adjoint:
- Related functors:
- nLab Link
This functor maps a monoid to the monoid ring , which consists of finite sums of elements in .
Satisfied Properties
Assigned properties
Deduced properties
Unsatisfied Properties
Assigned properties
- is not full
- is not essentially injective
- is not essentially surjective
- does not preserve terminal objects
- does not preserve equalizers
- is not cofinitary
- is not representable
Deduced properties*
- is not an equivalence
- is not continuous
- does not preserve finite products
- is not left exact
- is not left-invertible
- is not a right adjoint
- does not preserve products
- is not exact
- is not monadic
*This also uses the deduced satisfied properties.
Unknown properties
—