95.11 The stack in groupoids of finitely generated quasi-coherent sheaves
Let p : \mathcal{QC}\! \mathit{oh}_{fg} \to (\mathit{Sch}/S)_{fppf} be the stack introduced in Section 95.5 (using the abuse of notation introduced there). We can turn this into a stack in groupoids p' : \mathcal{QC}\! \mathit{oh}_{fg}' \to (\mathit{Sch}/S)_{fppf} by the procedure of Categories, Lemma 4.35.3, see Stacks, Lemma 8.5.3. In this particular case this simply means \mathcal{QC}\! \mathit{oh}_{fg}' has the same objects as \mathcal{QC}\! \mathit{oh}_{fg} but the morphisms are pairs (f, g) : (U, \mathcal{F}) \to (U', \mathcal{F}') where g is an isomorphism g : f^*\mathcal{F}' \to \mathcal{F}.
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