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September 2

(Co)monadicity of exponential adjunction

Given a nonempty set X, is it true that the adjunction $(-)\times X\dashv (-)^{X}$ is monadic and comonadic? More generally, when is this true for an object X of a Cartesian closed category C? GeoffreyT2000 (talk) 02:35, 2 September 2015 (UTC)[reply]