I've just seen Google suggests sites in a sort of "category" of results, as shown in the image below.
Any idea how to get listed in those results?
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The Google Carousel Results are powered by Google's knowledge graph. Now here is the kicker, there is no way to manually add data to the knowledge graph or request data to be added to it. Google adds data to their knowledge graph based on data sourced from authoritative websites such as Wikipedia, the Open Library Project, etc.
The best way to get yourself into the knowledge graph in the long term is to do everything that you should be doing for your website anyway, such as improving content, encouraging organic linking, gaining contextually relevant links, etc. As this happens and your ranking goes up your site will stand a better chance of being added to the knowledge graph, at which point Google's algorithms will evaluate what search queries will benefit from the return of your knowledge graph result.