MySQL 8.0

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CREATE TABLE tab(category  TEXT,	value INT);

INSERT INTO tab VALUES 
('A',	1),
('A',	1),
('A',	1),
('B',	0),
('B',	0),
('B',	1),
('C',	0),
('C',	0),
('C',	1)

Records: 9  Duplicates: 0  Warnings: 0


 SELECT category, BIT_AND(value) FROM tab GROUP BY category; 


category
BIT_AND(value)


A
1

B
0

C
0