To reduce or lower in rank or status, or to assign to a cottage (archaic).
From cotte (tunic/lowly garment) + -ise/-ize (verb suffix). The meaning evolved from the association of cottes with lower-class dress to mean 'to make lower in status.'
Medieval English literally let you 'cottise' someone—demote them socially—because clothing was rank-specific; changing someone's garment changed their entire social position!
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