free group functor
- Source: category of sets
- Target: category of groups
- nLab Link
This functor maps a set to the free group on that set.
Satisfied Properties
Properties from the database
- is conservative
- is faithful
- is a left adjoint
- is monomorphism-preserving
Deduced properties
Unsatisfied Properties
Properties from the database
- is not equalizer-preserving
- is not essentially surjective
- is not full
- is not terminal-object-preserving
Deduced properties*
- is not an equivalence
- is not continuous
- is not finite-product-preserving
- is not product-preserving
- is not left exact
- is not exact
- is not a right adjoint
- is not monadic
- is not representable
*This also uses the deduced satisfied properties.
Unknown properties
For these properties the database currently doesn't have an answer if they are satisfied or not. Please help to contribute the data!
- is cofinitary
- is comonadic