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since I needed the link to exist, I have created a stub for Morita morphism (of Lie groupoid)s. Made Hilsum-Skandalis morphism redirect to it, for the moment.
Here the literature is a little confused. Sometimes a Morita morphism (maybe this is only in one or two places) is a weak equivalence of Lie groupoids, so that an equivalence of stacks can be represented by a span of Morita morphisms. Sometimes it means a map in the localised bicategory $LieGpd[W^{-1}]$, where the ’left legs’ (pointing to the domain) are general weak equivalences. These are different to HS morphisms, which are right principal bibundles, which are saturated internal anafunctors. I know what you’re going to say - add it to the nLab! So I will. But not tonight.
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