nLab coexponential object




The notion of coexponential objects is dual to that of exponential objects.


Let XX and YY be objects of a category CC such that all binary coproducts with YY exist. (Usually, CC actually has all binary coproducts.) Then an coexponential object is an object Coexp(Y,X)Coexp(Y, X) equipped with a coevaluation map η:XCoexp(Y,X)Y\eta \colon X \to Coexp(Y, X) \coprod Y which is universal in the sense that, given any object ZZ and map e:XZYe\colon X \to Z \coprod Y, there exists a unique map u:Coexp(Y,X)Zu\colon Coexp(Y, X) \to Z such that e=(u,id Y)ηe = (u, id_Y) \circ \eta.

See also

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