Journal Article10.1016/j.jpaa.2024.107620
A homotopy coherent nerve for (∞,n)-categories
Lyne Moser,Nima Rasekh,Martina Rovelli +2 more
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TL;DR: A homotopy coherent nerve for (∞,n)-categories realizes a right Quillen equivalence between models of (∞,n)-categories and Segal category objects in (∞,n−1)-categories.
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Abstract: In the case of (∞,1)-categories, the homotopy coherent nerve gives a right Quillen equivalence between the models of simplicially enriched categories and of quasi-categories. This shows that homotopy coherent diagrams of (∞,1)-categories can equivalently be defined as functors of quasi-categories or as simplicially enriched functors out of the homotopy coherent categorifications. In this paper, we construct a homotopy coherent nerve for (∞,n)-categories. We show that it realizes a right Quillen equivalence between the models of categories strictly enriched in (∞,n−1)-categories and of Segal category objects in (∞,n−1)-categories. This similarly enables us to define homotopy coherent diagrams of (∞,n)-categories equivalently as functors of Segal category objects or as strictly enriched functors out of the homotopy coherent categorifications.
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Citations
Discreteness and completeness for $\Theta_n$-models of $(\infty,n)$-categories
Brendon Maongera
- 16 Sep 2022
TL;DR: In this paper , the authors establish cartesian model structures for variants of the $\Theta_n$-spaces in which they replace some or all of the completeness conditions by discreteness conditions.
References
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Daniel Dugger,David I. Spivak +1 more
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Higher quasi-categories vs higher Rezk spaces
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Homotopy-coherent algebra via Segal conditions
Hongyi Chu,Rune Haugseng +1 more
TL;DR: In this article, a general framework for algebraic patterns and their associated Segal objects, including conditions under which the latter are preserved by left and right Kan extensions, is presented, and sufficient conditions on a pattern O for free Segal O -spaces to be described by an explicit colimit formula are given.
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