The pullbacks of presheaves can be computed pointwise, and such computation determines the pullback, i.e. $F = G\times_S H$ iff $F(X) = G(X) \times_{S(X)} H(X)$ for all X. Does similar reduction holds for pullbacks of prestacks? We know that over $S$ the fiber of pullback is just the groupoid pullback of fibers, so we check the universality only restricting to morphisms over identity of $S$. Does that determine universal property of pullback, or we need to use the full formula every time (this involving tuple of 2 objects and arrow)?
2026-03-25 04:39:12.1774413552
Can one calculate pullback of prestacks fiberwise?
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