Is wearing a hat when running during the day on weekends also bad for hair loss?

I usually wear a hat whether I'm working or going anywhere.

I don't like it. But on weekend mornings or afternoons

If you walk outdoors, you won't wear a hat because of the UV rays

I couldn't help it, but I found that my scalp sweated a lot while running.

Does the hat being worn at this time also affect hair loss?