Kayı is a village in Daday District, in Kastamonu Province, Türkiye. Kayı lies at 1,053 m above sea level, in the Küre mountains. It has 126 inhabitants. The nearest city is Kastamonu, 47 km to the east. Among the landmarks around are Mahmut Bey Mosque (40 km) and Bonita (10.9 km).
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