Situation 99.5.1. Let S be a scheme. Let f : X \to B be a morphism of algebraic spaces over S. Assume that f is of finite presentation. We denote \mathcal{C}\! \mathit{oh}_{X/B} the category whose objects are triples (T, g, \mathcal{F}) where
T is a scheme over S,
g : T \to B is a morphism over S, and setting X_ T = T \times _{g, B} X
\mathcal{F} is a quasi-coherent \mathcal{O}_{X_ T}-module of finite presentation, flat over T, with support proper over T.
A morphism (T, g, \mathcal{F}) \to (T', g', \mathcal{F}') is given by a pair (h, \varphi ) where
h : T \to T' is a morphism of schemes over B (i.e., g' \circ h = g), and
\varphi : (h')^*\mathcal{F}' \to \mathcal{F} is an isomorphism of \mathcal{O}_{X_ T}-modules where h' : X_ T \to X_{T'} is the base change of h.
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