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The BM25 index accepts arrays of type text[] or varchar[]. 
CREATE TABLE array_demo (id SERIAL PRIMARY KEY, categories TEXT[]);
INSERT INTO array_demo (categories) VALUES
    ('{"food","groceries and produce"}'),
    ('{"electronics","computers"}'),
    ('{"books","fiction","mystery"}');

CREATE INDEX ON array_demo USING bm25 (id, categories)
WITH (key_field = 'id');
Under the hood, each element in the array is indexed as a separate entry. This means that an array is considered a match if any of its entries is a match. 
SELECT * FROM array_demo WHERE categories === 'food';
Expected Response
 id |           categories
----+--------------------------------
  1 | {food,"groceries and produce"}
(1 row)
Text arrays can be tokenized and filtered in the same way as text fields: 
CREATE INDEX ON array_demo USING bm25 (id, (categories::pdb.literal))
WITH (key_field = 'id');