I have read that a stack can just be thought of as a solution to a moduli problem, and there are some examples, like the stack of elliptic curves or the stack of vector bundles over a scheme $X$ such that there exists a universal family. Is there any criterion to know if given a stack there exists a universal family on it? More precisely, what happens with the stack of principal bundles over a curve? Does it carry a universal family?
2026-03-25 13:58:00.1774447080
Universal Family in the stack of principal bundles
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