This is what called a Barge cap or Breton Cap (Not to be confused with a Breton Hat which is a totally different hat shape)
Its also known as fiddler cap, Lenin cap, skipper cap, or mariner's cap, although that depends on if they have embroidery on the headband or peak.
Normally made of thick wool to provide the main stiffness, they are always peaked, they have firm wide headband, and usually come in black or navy blue.
Worn by 20th C merchant navy, barge owners and northern European factory workers.
The Fiddler cap name came about because of the film Fiddler on the Roof where the main character Topol wear one.
They came in to use in big way in Tsarists Russia due to the banning of Jewish style head ware.
Worn with with a black scarf it creates a ideal early 20th Century workers revolutionary look.
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