arXiv subjects

Mark Weber

Publications and source records attributed to Mark Weber.

39 records · Page 3Linked to original sources

arXiv2009

Free Products of Higher Operad Algebras

One of the open problems in higher category theory is the systematic construction of the higher dimensional analogues of the Gray tensor product of 2-categories. In this paper we continue the developments of [3] and [2] by understanding the natural generalisations of Gray's little brother, the funny tensor product of categories. In fact we exhibit for any higher categorical structure definable by an n-operad in the sense of Batanin [1], an analogous tensor product which forms a symmetric monoidal closed structure on the category of algebras of the operad.

math.CT↗

arXiv2008

Algebras of higher operads as enriched categories

We decribe the correspondence between normalised $ω$-operads and certain lax monoidal structures on the category of globular sets. As with ordinary monoidal categories, one has a notion of category enriched in a lax monoidal category. Within the aforementioned correspondence, we provide also an equivalence between the algebras of a given normalised $ω$-operad, and categories enriched in globular sets for the induced lax monoidal structure.

math.CT↗

arXiv2004

Operads within monoidal pseudo algebras

A general notion of operad is given, which includes as instances, the operads originally conceived to study loop spaces, as well as the higher operads that arise in the globular approach to higher dimensional algebra. In the framework of this paper, one can also describe symmetric and braided analogues of higher operads, likely to be important to the study of weakly symmetric, higher dimensional monoidal structures.

math.CT↗