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Undecidability of the Free Adjoint Construction

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Abstract

In this paper we discuss some aspects of categories obtained by freely adding right adjoints to all arrows in a category. We will give a description of the arrows and 2-cells in such a category and show how the equivalence relation on the 2-cells for an appropriately chosen category C A can be used to simulate a 2-register abacus A, so that deciding whether two 2-cells with different representatives are equal becomes equivalent to solving the halting problem for the abacus. In particular, this implies that (in general) equality of 2-cells in such categories is undecidable.

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Authors and Affiliations

  1. Department of Mathematics and Computing Science, Saint Mary's University, Hallifax, Nova Scotia, Canada, B3H 3C3

    R. J. MacG. Dawson

  2. Department of Mathematics and Statistics, Dalhousie University, Halifax, Nova Scotia, Canada, B3H 3J5

    R. Paré & D. A. Pronk

Authors
  1. R. J. MacG. Dawson
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  2. R. Paré
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  3. D. A. Pronk
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Dawson, R.J.M., Paré, R. & Pronk, D.A. Undecidability of the Free Adjoint Construction. Applied Categorical Structures 11, 403–419 (2003). https://doi.org/10.1023/A:1025712521140

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  • DOI: https://doi.org/10.1023/A:1025712521140

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