Group Object

A Monoid Object $(G,\cdot,0)$ in a Cartesian Category $\mathcal{C}$ is a group object when

• It is equipped with a morphism $\mathrm{neg}:G\to G$ such that

• $\mathrm{neg}$ is a left and right inverse to $\cdot$; EG: the following diagrams commute. \[

  \begin{tikzcd}

G && {G × G} && G

&& G \end{tikzcd} \]