Homotopy posets assemble into an oriented long exact sequence analogue and form layers of a categorical Postnikov tower, with Postnikov-complete (∞,∞)-categories identified as the limit of (∞,n)-categories along truncation functors.
A closed model structure for $n$-categories, internal $Hom$, $n$-stacks and generalized Seifert-Van Kampen
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abstract
We define a closed model category containing the $n$-nerves defined by Tamsamani, and admitting internal $Hom$. This allows us to construct the $n+1$-category $nCAT$ by taking the internal $Hom$ for fibrant objects. We prove a generalized Seifert-Van Kampen theorem for Tamsamani's Poincar\'e $n$-groupoid of a topological space. We give a still-speculative discussion of $n$-stacks, and similarly of comparison with other possible definitions of $n$-category.
fields
math.AT 2years
2026 2verdicts
UNVERDICTED 2representative citing papers
Proves an oriented Street-Roberts conjecture by presenting (∞,∞)-categories as sheaves on families of oriented polytopes, generalizing Campion's work.
citing papers explorer
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Homotopy Posets, Postnikov Towers, and Hypercompletions of $\infty$-Categories
Homotopy posets assemble into an oriented long exact sequence analogue and form layers of a categorical Postnikov tower, with Postnikov-complete (∞,∞)-categories identified as the limit of (∞,n)-categories along truncation functors.
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An Oriented Street--Roberts Conjecture
Proves an oriented Street-Roberts conjecture by presenting (∞,∞)-categories as sheaves on families of oriented polytopes, generalizing Campion's work.