Displaying similar documents to “Crossed semimodules and Schreier internal categories in the category of monoids.”

Left-Garside categories, self-distributivity, and braids

Patrick Dehornoy (2009)

Annales mathématiques Blaise Pascal

Similarity:

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,...

Internal object actions

Francis Borceux, George Z. Janelidze, Gregory Maxwell Kelly (2005)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

We describe the place, among other known categorical constructions, of the internal object actions involved in the categorical notion of semidirect product, and introduce a new notion of representable action providing a common categorical description for the automorphism group of a group, for the algebra of derivations of a Lie algebra, and for the actor of a crossed module.