Remark 99.14.5. Let B be an algebraic space over \mathop{\mathrm{Spec}}(\mathbf{Z}). Let B\textit{-Polarized} be the category consisting of triples (X \to S, \mathcal{L}, h : S \to B) where (X \to S, \mathcal{L}) is an object of \mathcal{P}\! \mathit{olarized} and h : S \to B is a morphism. A morphism (X' \to S', \mathcal{L}', h') \to (X \to S, \mathcal{L}, h) in B\textit{-Polarized} is a morphism (f, g, \varphi ) in \mathcal{P}\! \mathit{olarized} such that h \circ g = h'. In this situation the diagram
is 2-fibre product square. This trivial remark will occasionally be useful to deduce results from the absolute case \mathcal{P}\! \mathit{olarized} to the case of families over a given base algebraic space.
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