Limits in $n$-categories

Abstract

We define notions of direct and inverse limits in an $n$-category. We prove that the $n+1$-category $nCA{T}^{\prime }$ 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.

Approximately 90 pages

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• Algebraic (geometric) $n$-stacks
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Cited by in corpus (10)

• A Prehistory of n-Categorical Physics
• Structures in higher-dimensional category theory
• A Giraud-type characterization of the simplicial categories associated to closed model categories as $\infty$-pretopoi
• The periodic table of $n$-categories for low dimensions II: degenerate tricategories
• On the Breen-Baez-Dolan stabilization hypothesis for Tamsamani's weak n-categories
• On the moduli stack of commutative, 1-parameter formal Lie groups
• Iterated distributive laws
• Weak n-categories: opetopic and multitopic foundations
• Some properties of the theory of n-categories
• Secondary Kodaira-Spencer classes and nonabelian Dolbeault cohomology