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Department of Mathematics & Computer Science



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Introduction

This is a brief account of work of Brown and Heyworth [1] on extensions of rewriting methods.

The standard expression of such methods is in terms of words $ w$ in a free monoid $ \Delta^*$ on a set $ \Delta$. This may be extended to terms $ x\vert w$ where $ x$ belongs to a set $ X$ and the link between $ x$ and $ w$ is in terms of an action. More precisely, we suppose a monoid $ A$ acts on the set $ X$ on the right, and there is given a morphism of monoids $ F$: $ A\to B$ where $ B$ is given by a presentation with generating set $ \Delta$. The result of the rewriting will then be normal forms for the induced action of $ B$ on $ F_*(X)$. This gives an important extension of rewrite methods.

In fact monoids may be replaced by categories, and sets by directed graphs. This gives a formulation in terms of Kan extensions, or induced actions of categories, which we now explain.

Next: Presentations of Kan Extensions Up: paper10 Previous: paper10

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