Let $G$ be a topological groupoid with the property that any two isomorphic objects are topologically indistinguishable in $\mathrm{Ob}(G)$. Does that imply that $G$ is equivalent to a skeletal topological groupoid (where equivalence is meant in the sense defined here)?
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$\begingroup$ Note: this question already occured in a previous version of the linked thread, but I decided to remove it and put it in a separate question, since this question hasn't been answered in the linked thread, and the linked thread already contained too many other questions (all of which where answered!). $\endgroup$– user478652Commented Mar 21, 2022 at 12:50
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