Let $\mathbf{Grp}$ be a category of groups. Then, we know that there exists a coproduct $\bigsqcup_{I\in I} G_i$ for a family of groups $\{G_i\}_{I\in I}$ in $\mathbf{Grp}$ when $I$ is a finite set. This coproduct is given by a free product $G_1*\cdots * G_n$ if $I=\{1,\dots,n\}$. Now, I want t...

Let $\mathbf{Grp}$ be a category of groups. Then, we know that there exists a coproduct $\bigsqcup_{I\in I} G_i$ for a family of groups $\{G_i\}_{I\in I}$ in $\mathbf{Grp}$ when $I$ is a finite set. This coproduct is given by a free product $G_1*\cdots * G_n$ if $I=\{1,\dots,n\}$. Now, I want t...