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

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

1999-03-05

arxiv.org/abs/math/9903032v1

Mathematics

Combinatorics

31 pages, LaTeX2e, (submitted to JSC)

Scientific paper

The basic method of rewriting for words in a free monoid given a monoid presentation is extended to rewriting for paths in a free category given a `Kan extension presentation'. This is related to work of Carmody-Walters on the Todd-Coxeter procedure for Kan extensions, but allows for the output data to be infinite, described by a language. The result also allows rewrite methods to be applied in a greater range of situations and examples, in terms of induced actions of monoids, categories, groups or groupoids.

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