Abstract
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.
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Supported by the Claude Leon Foundation postdoctoral fellowship.
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Gray, J.R.A. Algebraic Exponentiation in General Categories. Appl Categor Struct 20, 543–567 (2012). https://doi.org/10.1007/s10485-011-9251-6
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DOI: https://doi.org/10.1007/s10485-011-9251-6
Keywords
- Adjoint functor
- Split extension
- Internal action
- Pullback functor
- Semi-abelian category
- Protomodular category
- (weakly) Mal’tsev category
- (weakly) Unital category