Notation 8.2.10. Let \(R\) be a discrete associative ring. We will from now on denote the categories \(\LMod _R(\Ab )\) and \(\RMod _R(\Ab )\) of discrete left and right \(R\)-modules by \(\LMod _R^{\heartsuit }\) and \(\RMod _R^{\heartsuit }\), respectively. This notation is justified by Lemma 8.2.9: these categories agree with the hearts of the t-structures on \(\LMod _R = \LMod _R(\Sp )\) and \(\RMod _R = \RMod _R(\Sp )\).
Tensor products in \(\Ab \) will from now on always be denoted by \(\otimes ^{\heartsuit }\); we reserve \(\otimes \) for the tensor product in \(\Sp \).
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