binary diagonal functor on the category of sets
- notation: : →
- Source: category of sets
- Target: category of pairs of sets
- Left adjoint:
- Right adjoint:
- Related functors:
- nLab Link
Every category has a (binary) diagonal functor , . Here, we specify that is the category of sets.
Satisfied Properties
Assigned properties
- is left-invertible
- is a left adjoint
- is a right adjoint
Deduced properties
- is continuous
- is conservative
- is essentially injective
- is faithful
- is cocontinuous
- is cofinitary
- is left exact
- preserves products
- is finitary
- preserves coproducts
- is right exact
- preserves finite products
- is exact
- preserves equalizers
- preserves monomorphisms
- preserves finite coproducts
- preserves coequalizers
- preserves epimorphisms
- preserves terminal objects
- preserves coreflexive equalizers
- preserves initial objects
- preserves reflexive coequalizers
- is monadic
- is comonadic
Unsatisfied Properties
Assigned properties
- is not full
- is not essentially surjective
- is not representable
Deduced properties*
- is not an equivalence
*This also uses the deduced satisfied properties.
Unknown properties
—