covariant power set functor
- Source: category of sets
- Target: category of sets
- nLab Link
This functor maps a set to its power set and a map of sets to the induced image operator .
Satisfied Properties
Properties from the database
Deduced properties
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Unsatisfied Properties
Properties from the database
- is not coequalizer-preserving
- is not equalizer-preserving
- is not essentially surjective
- is not finitary
- is not full
- is not initial-object-preserving
- 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
- is not cocontinuous
- is not finite-coproduct-preserving
- is not coproduct-preserving
- is not right exact
- is not a left adjoint
- is not comonadic
*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