Computable étale spaces over a computable space Y are equivalent to computable maps from Y into the effective category ODS of overt-discrete quasi-Polish spaces, with a generalization to computable category actions.
Chen,Borel functors, interpretations, and strong conceptual completeness for Lω1ω, Transactions of the American Mathematical Society372(2019), 8955–8983
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A note on computable \'{e}tale spaces
Computable étale spaces over a computable space Y are equivalent to computable maps from Y into the effective category ODS of overt-discrete quasi-Polish spaces, with a generalization to computable category actions.