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.
de Brecht,Quasi-Polish spaces, Annals of Pure and Applied Logic164(2013), 356–381
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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.