Definition:Fundamental Group Functor

Definition
Let $\mathbf{Top}^*$ be the category of pointed topological spaces.

Let $\mathbf{Grp}$ be the category of groups.

The fundamental group functor is the covariant functor $\pi_1 : \mathbf{Top}^* \to \mathbf{Grp}$ with:

Also see

 * Definition:Homotopy Group Functor