fundamental group functor

 topology
Notation π1:Top∗→Grp\pi_1: \Top_* \to \Grp Domain category of pointed topological spacesCodomain category of groups Related π0\pi_0 External nLab Link

The fundamental group π1(X,x0)\pi_1(X,x_0) of a pointed topological space (X,x0)(X,x_0) is the group of homotopy classes of loops at x0x_0. The group operation is concatenation of paths. For example, we have π1(S1,1)≅Z\pi_1(S^1,1) \cong \IZ (see Hatcher's Algebraic Topology, Theorem 1.7).

Satisfied Properties

Assigned properties

Deduced properties

Unsatisfied Properties

Assigned properties

Deduced properties*

*This also uses the deduced satisfied properties.

Unknown properties

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