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Microsoft Cloud Hybrid Search Service Application is a hybrid enterprise search capability that enables organizations to search both on-premises and cloud-based data repositories without generated siloed results.
Previously, to generate results from these multiple but siloed data sources would require federated search, which enables a user to submit a query and return unified results. Nonetheless, federated search has been clunky and not user-friendly. The Cloud Hybrid Search Service Application is Microsoft's attempt to create a more user-friendly interface for search results.