walking isomorphism object inclusion
This is the natural embedding of the trivial category with a single object into the walking isomorphism given by two objects and an isomorphism . This is the simplest example of an equivalence of categories which is not an isomorphism.
Satisfied Properties
Assigned properties
Deduced properties
- is a coreflector
- is an equivalence
- is continuous
- preserves equalizers
- preserves coreflexive equalizers
- preserves binary products
- is faithful
- is full
- is conservative
- is dominant
- is right-invertible
- is essentially injective
- is full on isomorphisms
- preserves monomorphisms
- is a reflector
- is cocontinuous
- preserves coequalizers
- preserves reflexive coequalizers
- preserves binary coproducts
- preserves epimorphisms
- is a right adjoint
- is a left adjoint
- preserves terminal objects
- is left-invertible
- is monadic
- is cofinitary
- is left exact
- preserves products
- preserves regular monomorphisms
- is pseudomonic
- preserves initial objects
- is comonadic
- is finitary
- preserves coproducts
- is right exact
- preserves regular epimorphisms
- preserves finite products
- is exact
- is regular
- preserves finite coproducts
- is coregular
Unsatisfied Properties
Assigned properties
- is not an isomorphism
Deduced properties*
- is not representable
*This also uses the deduced satisfied properties.
Unknown properties
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