From Basic Category Theory for Computer Scientists
Let $C$ be a category with all binary products and let $A$ and $B$ be objects of $C$. An object $B^A$ is an exponential object if there is an arrow $eval_{AB} : (B^A \times A) \to B$ such that for any object $C$ and arrow $g: (C \times A)\to B$ there is a unique arrow $curry(g): C \to B^A$ such that $eval_{AB} \circ(curry(g) \times id_A) =g$.
How is its dual concept "coexponential" defined?
By reversing the three arrows in the diagram, according to https://ncatlab.org/nlab/show/exponential+object
Dually, a coexponential object in CC is an exponential object in the opposite category C opC^{op}.
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Thanks.