Abstract
We show that in an ideal-determined unital category the Higgins commutator can be characterized as the largest binary operation C on subobjects (defined on all subobjects of each object) satisfying the following conditions: (a) C is order-preserving; (b) C(H, K) is always less or equal to the meet of normal closures of H and K; (c) \(C(f(H),f(K))=f(C(H,K))\) for every pair of subobjects H and K of an object X, and every morphism f whose domain is X.
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Acknowledgements
This work forms part of the author’s Ph.D. thesis at Stellenbosch university, under the supervision of J.R.A. Gray. Funding was provided by Deutscher Akademischer Austauschdienst (Grant No. 91560461).
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George Janelidze.
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Shaumbwa, V.T. A Characterization of the Higgins Commutator. Appl Categor Struct 27, 159–162 (2019). https://doi.org/10.1007/s10485-018-9548-9
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DOI: https://doi.org/10.1007/s10485-018-9548-9