forgetful functor for vector spaces
- Source: category of vector spaces
- Target: category of sets
- nLab Link
This functor maps a vector space (over a fixed field ) to its underlying set .
Satisfied Properties
Properties from the database
- is conservative
- is epimorphism-preserving
- is finitary
- is monadic
- is representable
Deduced properties
- is faithful
- is a right adjoint
- is continuous
- is cofinitary
- is equalizer-preserving
- is product-preserving
- is finite-product-preserving
- is terminal-object-preserving
- is left exact
- is monomorphism-preserving
Unsatisfied Properties
Properties from the database
- is not coequalizer-preserving
- is not essentially surjective
- is not initial-object-preserving
Deduced properties*
- is not an equivalence
- is not full
- is not cocontinuous
- is not finite-coproduct-preserving
- is not coproduct-preserving
- is not right exact
- is not exact
- is not a left adjoint
- is not comonadic
*This also uses the deduced satisfied properties.
Unknown properties
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