I was inspecting the wordpress schema and I observed this:

Why is term_taxonomy_id assigned as a primary key as well as an index? Are there any benefits of it?
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If the PRIMARY index is a primary key, that will enforce that there can be only one combination of object_id and term_taxonomy_id in the table. Since object_id appears first, queries referencing object_id will use the structure of the index to query values very quickly. If queries don’t reference any other fields, they won’t even have to look at table data since the data is all in the index.
If term_taxonomy_id is used for queries however, the entire index would have to be scanned to find the rows. Having an index on term_taxonomy_id will make those queries run very fast.