trivial functor from the walking idempotent
- Notation:
- Domain: walking idempotent
- Codomain: trivial category
- Related functors: , ,
Every category has a unique functor into the trivial category. Here, we specify that is the walking idempotent. It is a basic example of an essentially injective functor which is not conservative.
Satisfied Properties
Assigned properties
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Deduced properties
- is continuous
- preserves equalizers
- is essentially surjective
- is right-invertible
- is full
- is essentially injective
- is full on isomorphisms
- is cocontinuous
- preserves coequalizers
- is cofinitary
- is left exact
- preserves products
- preserves coreflexive equalizers
- preserves regular monomorphisms
- is dominant
- is finitary
- preserves coproducts
- is right exact
- preserves reflexive coequalizers
- preserves regular epimorphisms
- preserves finite products
- is exact
- preserves monomorphisms
- is regular
- preserves finite coproducts
- preserves epimorphisms
- is coregular
- preserves binary products
- preserves terminal objects
- preserves binary coproducts
- preserves initial objects
Unsatisfied Properties
Assigned properties
- is not conservative
- is not a left adjoint
- is not a right adjoint
Deduced properties*
- is not a reflector
- is not fully faithful
- is not faithful
- is not left-invertible
- is not monadic
- is not a coreflector
- is not comonadic
- is not an equivalence
- is not pseudomonic
- is not an isomorphism
- is not representable
*This also uses the deduced satisfied properties.
Unknown properties
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