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Vertically iterated classical enrichment

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Stefan Forcey

Lyubashenko has described enriched 2-categories as categories enriched
over V-Cat, the 2-category of categories enriched over a
symmetric monoidal V. This construction is the strict analogue for
V-functors in V-Cat of Brian Day's probicategories for
V-modules in V-Mod. Here I generalize the strict version to enriched
n-categories for k-fold monoidal V. The latter is defined
as by Balteanu, Fiedorowicz, Schwanzl and Vogt but with the addition of
making visible the coherent associators. The
symmetric case can easily be recovered. This paper proposes a recursive
definition of V-n-categories and their morphisms. We show that
for V k-fold monoidal the structure of a (k-n)-fold monoidal strict
(n+1)-category is possessed by V-n-Cat. This article is a
completion of the work begun by the author in the preprint entitled
Higher dimensional enrichment (math.CT/0306086), and the initial
sections duplicate the beginning of that paper.

Keywords:
enriched categories, n-categories, iterated monoidal categories

2000 MSC:
18D10; 18D20

*Theory and Applications of Categories,*
Vol. 12, 2004,
No. 10, pp 299-325.

http://www.tac.mta.ca/tac/volumes/12/10/12-10.dvi

http://www.tac.mta.ca/tac/volumes/12/10/12-10.ps

http://www.tac.mta.ca/tac/volumes/12/10/12-10.pdf

ftp://ftp.tac.mta.ca/pub/tac/html/volumes/12/10/12-10.dvi

ftp://ftp.tac.mta.ca/pub/tac/html/volumes/12/10/12-10.ps

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