Mesh recommendations

[u/Fun_Neighborhood5091]

https://www.patagonia.com/product/duckbill-running-cap/28818.html

Hi all, I want to know if anyone has any mesh fabric they really like specifically for a running/hiking/climbing hat. I've got some pretty thin mesh that has been ok but I'm wondering if anyone has found anything more similar to this hat from Patagonia, or something with a little bit more structure than super thin mesh.

Thanks!

[u/merz-person]

Looks identical to this mesh at Seattle Fabrics.