free group functor
- notation: : →
- Source: category of sets
- Target: category of groups
- Right adjoint:
- Related functors: ,
- nLab Link
This functor maps a set to the free group on that set. In the proofs, we abbreviate .
Satisfied Properties
Assigned properties
- is a left adjoint
- is conservative
- preserves monomorphisms
- preserves coreflexive equalizers
- is essentially injective
Deduced properties
Unsatisfied Properties
Assigned properties
- is not full
- is not essentially surjective
- does not preserve terminal objects
- does not preserve equalizers
- is not cofinitary
- is not left-invertible
- is not representable
Deduced properties*
- is not an equivalence
- is not continuous
- does not preserve finite products
- is not left exact
- is not a right adjoint
- does not preserve products
- is not exact
- is not monadic
*This also uses the deduced satisfied properties.
Unknown properties
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