Using Rewriting Systems to Compute Left Kan Extensions and Induced Actions of Categories

Left Kan Extensions Over !-Cat

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...

Rewriting procedures generalise to Kan extensions of actions of categories

kan A package for Induced Category Actions

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...

2 3 Ju n 19 99 Using Automata to obtain Regular Expressions for Induced Actions ∗

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...

Gröbner Basis Techniques for Computing Actions of K - Categories ∗

This paper involves categories and computer science. Gröbner basis theory is a branch of computer algebra which has been usefully applied to a wide range of problems. Kan extensions are a key concept of category theory capable of expressing most algebraic structures. The paper combines the two, using Gröbner basis techniques to compute certain kinds of Kan extension.