path components functor
- notation:
- Source: category of topological spaces
- Target: category of sets
- Related functors: ,
- nLab Link
This functor maps a topological space to its set of path components. Thus, , where is the underlying set and when there is a path from to .
Satisfied Properties
Assigned properties
Deduced properties
Unsatisfied Properties
Assigned properties
- is not conservative
- is not faithful
- is not full
- is not essentially injective
- does not preserve regular monomorphisms
- is not cofinitary
- is not finitary
Deduced properties*
- is not continuous
- does not preserve equalizers
- does not preserve monomorphisms
- does not preserve coreflexive equalizers
- is not fully faithful
- is not left-invertible
- is not full on isomorphisms
- is not pseudomonic
- is not monadic
- is not cocontinuous
- is not coregular
- is not comonadic
- is not a right adjoint
- is not an equivalence
- is not left exact
- is not representable
- is not a left adjoint
- does not preserve coequalizers
- is not a reflector
- is not an isomorphism
- is not exact
- is not regular
- is not a coreflector
- is not right exact
- does not preserve reflexive coequalizers
*This also uses the deduced satisfied properties.
Unknown properties
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