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Algebraic Exponentiation in General Categories

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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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Authors and Affiliations

  1. Department of Mathematical Sciences (Mathematics Division), University of Stellenbosch, Private Bag X1, Matieland, 7602, South Africa

    James Richard Andrew Gray

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  1. James Richard Andrew Gray
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Correspondence to James Richard Andrew Gray.

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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

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