The rigidity of fungal hyphal walls is primarily attributed to chitin, a complex polysaccharide, along with other polysaccharides like glucans, and proteins, which together form a robust structural framework. 

This is a major structural component of fungal cell walls, similar to how it forms the exoskeleton of insects and crustaceans. Chitin is a homopolymer of β-1,4-linked N-acetylglucosamine units, providing significant strength and rigidity.