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 relationship 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, Birkhaüser (2000), Chap. IX].
@article{AMBP_2009__16_2_189_0, author = {Dehornoy, Patrick}, title = {Left-Garside categories, self-distributivity, and braids}, journal = {Annales math\'ematiques Blaise Pascal}, volume = {16}, year = {2009}, pages = {189-244}, doi = {10.5802/ambp.263}, zbl = {1183.18004}, mrnumber = {2568862}, language = {en}, url = {http://dml.mathdoc.fr/item/AMBP_2009__16_2_189_0} }
Dehornoy, Patrick. Left-Garside categories, self-distributivity, and braids. Annales mathématiques Blaise Pascal, Tome 16 (2009) pp. 189-244. doi : 10.5802/ambp.263. http://gdmltest.u-ga.fr/item/AMBP_2009__16_2_189_0/
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