fundamental group functor
- notation:
- Source: category of pointed topological spaces
- Target: category of groups
- Related functors:
- nLab Link
The fundamental group of a pointed topological space is the group of homotopy classes of loops at . The group operation is concatenation of paths. For example, we have (see Hatcher's Algebraic Topology, Theorem 1.7).
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
- does not preserve regular epimorphisms
- does not preserve binary coproducts
- is not finitary
- is not cofinitary
Deduced properties*
- is not continuous
- does not preserve equalizers
- does not preserve monomorphisms
- does not preserve coreflexive equalizers
- is not regular
- is not fully faithful
- is not left-invertible
- is not full on isomorphisms
- is not pseudomonic
- is not monadic
- is not cocontinuous
- does not preserve finite coproducts
- does not preserve coequalizers
- does not preserve epimorphisms
- does not preserve reflexive coequalizers
- 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 coproducts
- is not right exact
- is not a reflector
- is not an isomorphism
- is not exact
- is not a coreflector
*This also uses the deduced satisfied properties.
Unknown properties
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