squaring functor on sets
- notation: : →
- Source: category of sets
- Target: category of sets
- Left adjoint:
- Related functors: , ,
This functor maps a set to its square . It is a simple example of a polynomial functor.
Satisfied Properties
Assigned properties
- preserves initial objects
- preserves epimorphisms
- is representable
- is a right adjoint
- is conservative
- is finitary
- preserves reflexive coequalizers
- is essentially injective
Deduced properties
Unsatisfied Properties
Assigned properties
- is not full
- is not essentially surjective
- does not preserve coequalizers
- is not left-invertible
Deduced properties*
- is not an equivalence
- is not right exact
- does not preserve finite coproducts
- is not exact
- is not cocontinuous
- does not preserve coproducts
- is not a left adjoint
- is not comonadic
*This also uses the deduced satisfied properties.
Unknown properties
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