Algebras of Higher Operads as Enriched Categories

Algebras of Higher Operads as Enriched Categories

One of the open problems in higher category theory is the systematic construction of the higher dimensional analogues of the Gray tensor product. In this paper we begin to adapt the machinery of globular operads [1] to this task. We present a general construction of a tensor product on the category of n-globular sets from any normalised (n + 1)-operad A, in such a way that the algebras for A ma...

Algebras of higher operads as enriched categories II

One of the open problems in higher category theory is the systematic construction of the higher dimensional analogues of the Gray tensor product. In this paper we continue the work of [7] to adapt the machinery of globular operads [4] to this task. The resulting theory includes the Gray tensor product of 2-categories and the Crans tensor product [12] of Gray categories. Moreover much of the pre...

5 M ar 2 00 8 Algebras of higher operads as enriched categories

We decribe the correspondence between normalised ω-operads in the sense of [1] 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 ωoperad, and categories enri...

Higher Operads, Higher Categories

algebras , operads and tensor categories

We study the operadic and categorical formulations of (conformal) full field algebras. In particular, we show that a grading-restricted R × R-graded full field algebra is equivalent to an algebra over a partial operad constructed from spheres with punctures and local coordinates. This result is generalized to conformal full field algebras over V L ⊗ V R , where V L and V R are two vertex operat...