How do you show that the fundamental groupoid $\Pi(S^1 \vee S^1) \simeq \mathbb{Z} \star \mathbb{Z}$? I understand how to do so in the case of groups, but don't totally understand what's going on in the case of groupoids?
I feel I'm a bit confused about the difference between the fundamental group and groupoid. I suppose the answer that was deleted was confused as well...