Dreaming of a cat laying beside you while you sleep can have various interpretations. Cats often symbolize independence, intuition, and comfort. Here are a few insights into your dream:

1. Comfort and Companionship: The presence of the cat may represent a sense of comfort and security in your life. It could indicate that you are in a phase where you value companionship and the soothing presence of others.
2. Intuition and Femininity: Cats are often associated with feminine energy and intuition. This dream might suggest that you should trust your instincts more or pay attention to your inner feelings and insights.
3. Independence: Cats are known for their independent nature. This dream could reflect your own desire for independence or a reminder to embrace your self-sufficiency.
4. Relaxation and Peace: If the cat seemed peaceful and content, it might signify a period of relaxation and tranquility in your waking life.

Consider your feelings during the dream and your current life circumstances for a more personalized interpretation. If the cat has any particular significance to you, that can also influence the meaning of your dream.