In Jainism, the term "Kay" (often spelled as "Kāy" or "Kāya") refers to "body" or "type of body." According to Jain teachings, there are five kinds of bodies (Panch-kāya) in which living beings (jivas) can exist. These are known as the Panchendriya Jivas (five-bodied beings):

1. Ekendriya (One-sensed beings): Beings with only the sense of touch (e.g., earth-bodied, water-bodied, fire-bodied, air-bodied, and plant-bodied beings).
2. Dvindriya (Two-sensed beings): Beings with touch and taste senses (e.g., worms).
3. Trindriya (Three-sensed beings): Beings with touch, taste, and smell senses (e.g., ants).
4. Chaturindriya (Four-sensed beings): Beings with touch, taste, smell, and sight senses (e.g., bees).
5. Panchendriya (Five-sensed beings): Beings with all five senses: touch, taste, smell, sight, and hearing (e.g., humans, animals).

Additionally, in Jain cosmology, Kay is sometimes used to refer to the classification of living beings based on the body they possess:

1. Prithvikaya (Earth-bodied)
2. Apkaya (Water-bodied)
3. Teukaya (Fire-bodied)
4. Vayukaya (Air-bodied)
5. Vanaspatikaya (Plant-bodied)

So, in summary, Jainism recognizes five types of Kay (bodies) in which souls can exist.