given f : X \to Y in \mathcal{P} and Y' \to Y general, then X \times _ Y Y' exists and X \times _ Y Y' \to Y' is in \mathcal{P},
given f : X \to Y in \mathcal{P} and Y' \to Y general, then X \times _ Y Y' exists and X \times _ Y Y' \to Y' is in \mathcal{P},
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