Limits in $n$-categories

Details Limits in $n$-categories Limits in $n$-categories

1997-08-07

arxiv.org/abs/alg-geom/9708010v1

Mathematics

Algebraic Geometry

Approximately 90 pages

Scientific paper

We define notions of direct and inverse limits in an $n$-category. We prove that the $n+1$-category $nCAT'$ of fibrant $n$-categories admits direct and inverse limits. At the end we speculate (without proofs) on some applications of the notion of limit, including homotopy fiber product and homotopy coproduct for $n$-categories, the notion of $n$-stack, representable functors, and finally on a somewhat different note, a notion of relative Malcev completion of the higher homotopy at a representation of the fundamental group.

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