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