منابع مشابه
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...
متن کاملAlgebras 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...
متن کاملHigher Enrichment: N-fold Operads and Enriched N-categories, Delooping and Weakening
The most familiar example of higher, or vertically iterated enrichment is that in the definition of strict n-category. We begin with strict n-categories based on a general symmetric monoidal category V. Motivation is offered through a comparison of the classical and extended versions of topological quantum field theory. A sequence of categorical types that filter the category of monoidal catego...
متن کامل5 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...
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 2020
ISSN: 0001-8708
DOI: 10.1016/j.aim.2019.106913