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Scarlet was a type of fine and expensive woollencloth common in MedievalEurope. The word "scarlet" is derived from Old French "escarlate" (itself derived from Low Latin and Persian).
Scarlet cloth was produced in red, white, blue, green, and brown colors, among others. The most common color was carmine red, though, which resulted in the double meaning of the word as a color designation.
It is probable that name of the character Will Scarlett in the Robin Hood legends referred to this type of cloth, similarly to the common occupational surnames (e.g. Weaver, Cooper, Fletcher, etc.).