Higher Dimensional Enrichment

Details Higher Dimensional Enrichment Higher Dimensional Enrichment

2003-06-04

arxiv.org/abs/math/0306086v2

Mathematics

Category Theory

50 pages; complete definition of V-n-categories and morphisms between them; journal style and notation--note tensor^(1) replac

Scientific paper

Lyubashenko has described enriched 2-categories as categories enriched over V-Cat, the 2-category of categories enriched over a symmetric monoidal V. I have generalized this to the k-fold monoidal V. The symmetric case can easily be recovered. The introduction of this paper proposes a recursive definition of V-n-categories and their morphisms. Then I consider the special case of V-2-categories and give the details of the proof that with their morphisms these form the structure of a 3-category.

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