Document Zbl 0941.18005 - zbMATH Open
Using rewriting systems to compute left Kan extensions and induced actions of categories. (English) Zbl 0941.18005
Summary: The aim is to apply string-rewriting methods to compute left Kan extensions or equivalently, induced actions of monoids, categories, groups or groupoids. This allows rewriting methods to be applied to a greater range of situations and examples than before. The data for the rewriting is called a Kan extension presentation. The paper has its origins in earlier work by Carmody and Walters who gave an algorithm for computing left Kan extensions based on extending the Todd-Coxeter procedure, an algorithm only applicable when the induced action is finite. The current work, in contrast, gives information even when the induced action is infinite.
MSC:
| 18A40 | Adjoint functors (universal constructions, reflective subcategories, Kan extensions, etc.) |
| 68Q42 | Grammars and rewriting systems |
| 18-04 | Software, source code, etc. for problems pertaining to category theory |
References:
| [1] | Baader, F.; Nipkow, T., Term Rewriting and All That (1998), Cambridge University Press: Cambridge University Press New York |
| [2] | Book, R. V.; Otto, F., String-Rewriting Systems (1993), Springer: Springer New York · Zbl 0832.68061 |
| [3] | Bush, M. R.; Leeming, M.; Walters, R. F.C, Computing left Kan extensions, J. Symb. Comput., 11, 11-20 (1997) · Zbl 1038.18003 |
| [4] | S. Carmody, R. F. C. Walters, Research Reports of the School of Mathematics and Statistics, The University of Sydney 90-19; S. Carmody, R. F. C. Walters, Research Reports of the School of Mathematics and Statistics, The University of Sydney 90-19 |
| [5] | S. Carmody, R. F. C. Walters, Category Theory, Proceedings of the International Conference, Como, Italy, 22-28 July 1990, LNM 1488; S. Carmody, R. F. C. Walters, Category Theory, Proceedings of the International Conference, Como, Italy, 22-28 July 1990, LNM 1488 |
| [6] | Epstein, D. B.A; Cannon, J. W., Word Processing in Groups (1992), Jones and Bartlett Publishers: Jones and Bartlett Publishers Boston · Zbl 0764.20017 |
| [7] | M. Fleming, R. Gunther, R. Rosebrugh, anonymous ftp://sun1.mta.ca/pub/papers/rosebrugh/catdsalg.dvi,tex and/catuser.dvi,tex; M. Fleming, R. Gunther, R. Rosebrugh, anonymous ftp://sun1.mta.ca/pub/papers/rosebrugh/catdsalg.dvi,tex and/catuser.dvi,tex |
| [8] | A. Heyworth, 1998; A. Heyworth, 1998 |
| [9] | Holt, D. F., Knuth-Bendix in Monoids and Automatic Groups (1996), University of Warwick |
| [10] | Holt, D. F.; Hurt, D. F., Computing automatic coset systems and subgroup presentations, J. Symb. Comput., 27, 1-19 (1999) · Zbl 0930.20035 |
| [11] | Hopcroft, J.; Ullman, J., Introduction to Automata Theory, Languages and Computation (1979), Addison-Wesley: Addison-Wesley Reading, MA · Zbl 0426.68001 |
| [12] | Mac Lane, S., Categories for the Working Mathematician (1971), Springer-Verlag: Springer-Verlag New York · Zbl 0232.18001 |
| [13] | Mitchell, B., Rings with several objects, Adv. Math., 8, 1-161 (1972) · Zbl 0232.18009 |
| [14] | Mora, T., Gröbner Bases and the Word Problem (1987), University of Genova (manuscript) |
| [15] | I. D. Redfern, 1993; I. D. Redfern, 1993 |
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