Algebraic Exponentiation in General Categories
We study a categorical-algebraic concept of exponentiation, namely, right adjoints for the pullback functors between D. Bourn's categories of points. We introduce and study them in the situations where the ordinary pullback functors between bundles do not admit right adjoints-in particular, for semi-abelian, protomodular, (weakly) Mal'tsev, (weakly) unital, and more general categories. We present a number of examples and counter examples for the existence of such right adjoints. © 2011 Springer Science+Business Media B.V.