Algebraic Exponentiation in General Categories

作者：Gray James Richard Andrew^*

来源：Applied Categorical Structures, 2012, 20(6): 543-567.

DOI：10.1007/s10485-011-9251-6

• Adjoint functor
• Split extension
• Internal action
• Pullback functor
• Semi-abelian category
• Protomodular category
• (weakly) Mal%26apos
• tsev category
• (weakly) Unital category

We study a categorical-algebraic concept of exponentiation, namely, right adjoints for the pullback functors between D. Bourn%26apos;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%26apos;tsev, (weakly) unital, and more general categories. We present a number of examples and counter examples for the existence of such right adjoints.

• 出版日期2012-12