Philippe Malbos
Coherent presentations and actions on categories.
Tue, 03/27/2012 - 15:01 — SomNambulAuthors: Yves Guiraud, Philippe Malbos, Stéphane Gaussent
Subjects: Category Theory
AbstractWe study Deligne's notion of action of a monoid on a category and, in
particular, the piece of data that corresponds to the coherence relations that
such an action should satisfy. We prove that actions of a monoid are equivalent
to 2-functors from a 2-categorical cofibrant replacement of the monoid into the
2-category of categories.Identities among relations for higher-dimensional rewriting systems.
Mon, 10/26/2009 - 14:11 — SomNambulAuthors: Yves Guiraud, Philippe Malbos
Subjects: Category Theory
AbstractWe generalize the notion of identities among relations, well known for
presentations of groups, to presentations of n-categories by polygraphs. To
each polygraph, we associate a track n-category, generalizing the notion of
crossed module for groups, in order to define the natural system of identities
among relations. We relate the facts that this natural system is finitely
generated and that the polygraph has finite derivation type.
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