Definition 5.3.6 (Commutative group). A commutative monoid \(M\) is called a commutative group if the shear map \((\pr _1,+)\colon M \times M \to M \times M\) is an isomorphism. We denote by \[ \CGrp (C) \quad \subseteq \quad \CMon (C) \] the full subcategory spanned by the commutative groups in \(C\).
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