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arXiv · 0810.4698

Left-Garside categories, self-distributivity, and braids

Patrick Dehornoy
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Abstract

In connection with the emerging theory of Garside categories, we develop the notions of a left-Garside category and of a locally left-Garside monoid. In this framework, the connection between the self-distributivity law LD and braids amounts to the result that a certain category associated with LD is a left-Garside category, which projects onto the standard Garside category of braids. This approach leads to a realistic program for establishing the Embedding Conjecture of [Dehornoy, Braids and Self-distributivity, Birkhauser (2000), Chap. IX].

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Patrick Dehornoy. 2008-10-26. Left-Garside categories, self-distributivity, and braids. https://arxiv.org/abs/0810.4698

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