monoid ring functor
This functor maps a monoid to the monoid ring , which consists of finite sums of elements in .
Satisfied properties
Assigned properties
- is a left adjoint
- is conservative
- preserves monomorphisms
- preserves coreflexive equalizers
Deduced properties
- preserves regular monomorphisms
- is cocontinuous
- is comonadic
- is finitary
- preserves coproducts
- is right exact
- is faithful
- preserves finite coproducts
- preserves coequalizers
- preserves epimorphisms
- is coregular
- preserves binary coproducts
- preserves initial objects
- preserves reflexive coequalizers
- preserves regular epimorphisms
Unsatisfied properties
Assigned properties
- is not full
- is not essentially injective
- is not dominant
- does not preserve terminal objects
- does not preserve equalizers
- is not cofinitary
Deduced properties*
- is not a reflector
- is not continuous
- does not preserve finite products
- is not left exact
- does not preserve binary products
- is not fully faithful
- is not left-invertible
- is not full on isomorphisms
- is not essentially surjective
- is not a right adjoint
- is not an equivalence
- does not preserve products
- is not exact
- is not representable
- is not regular
- is not right-invertible
- is not pseudomonic
- is not an isomorphism
- is not monadic
- is not a coreflector
*This also uses the deduced satisfied properties.
Unknown properties
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