| Popis: |
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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