Definition 5.1.5. We say that a monoid \(M \in \Mon (C)\) is grouplike, or a group in \(C\), if the so-called shear map \[ (\pr _1,m)\colon M \times M \to M \times M, \qquad (x,y) \mapsto (x,xy) \] is an isomorphism in \(C\). We denote by \(\Grp (C) \subseteq \Mon (C)\) the full subcategory spanned by the groups in \(C\).
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