Rewriting procedures generalise to Kan extensions of actions of categories
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منابع مشابه
Using Rewriting Systems to Compute Left Kan Extensions and Induced Actions of Categories
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 ga...
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An existing procedure to compute left Kan extensions over the ground category Set also computes left Kan extensions over the ground categories Cat, 2-Cat, n-Cat for any n and indeed !-Cat. Therefore extension data struc-tured in this manner already can make use of the left Kan extension notion of a best possible approximation. Examples include systems of labeled transition systems and certain h...
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Presentations of Kan extensions of category actions provide a natural framework for expressing induced actions, and therefore a range of different combinatorial problems. Rewrite systems for Kan extensions have been defined and a variation on the Knuth-Bendix completion procedure can be used to complete them – when possible. Regular languages and automata are a useful way of expressing sets and...
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The kan package was originally implemented in 1997 using the GAP 3 language, to compute induced actions of categories, when the first author was studying for a Ph.D. in Bangor. This reduced version only provides functions for the computation of normal forms of representatives of double cosets of finitely presented groups. Bug reports, suggestions and comments are, of course, welcome. Please con...
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Continuous lattices were characterised by Mart́ın Escardó as precisely the objects that are Kan-injective w.r.t. a certain class of morphisms. We study Kan-injectivity in general categories enriched in posets. An example: ω-CPO’s are precisely the posets that are Kan-injective w.r.t. the embeddings ω →֒ ω + 1 and 0 →֒ 1. For every class H of morphisms we study the subcategory of all objects Kan-in...
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تاریخ انتشار 1999