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Under which conditions can we say that the cotensor objects in a (closed) V-category are the exponential objects? It is just when V=Set?

Under which conditions can we say that the cotensor objects in a (closed) V-category are the exponential objects?

Under which conditions can we say that the cotensor objects in a (closed) V-category are the exponential objects? It is just when V=Set?

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Cotensor vs exponential objects.

Under which conditions can we say that the cotensor objects in a (closed) V-category are the exponential objects?