Previous |  Up |  Next

Article

Keywords:
Gray tensor product; saturated $n$-complicial set; $(\infty,n)$-category
Summary:
We show that the pretensor and tensor products of simplicial sets with marking are compatible with the homotopy theory of saturated N-complicial sets (which are a proposed model of $(\infty,n)$-categories), in the form of a Quillen bifunctor and a homotopical bifunctor, respectively.
References:
[1] Ara, Dimitri, Lucas, Maxime: The folk model category structure on strict \omega-categories is monoidal. Theory Appl. Categ., Vol. 35, Paper No. 21, 745-808 MR 4105933
[2] Campion, Tim, Kapulkin, Chris, Maehara, Yuki: A cubical model for (\infty, n)-categories. arXiv:2005.07603 MR 4918105
[3] Crans, Sjoerd E.: Pasting schemes for the monoidal biclosed structure on \omega-\mathbf{Cat}. Part of PhD Thesis available at https://citeseerx.ist.psu.edu/viewdoc/download;jsessionid=3484DE4DE7D1AB400C82F3416FCED03B?doi=10.1.1.56.8738&rep=rep1&type=pdf, retrieved August 2022
[4] Gagna, Andrea, Harpaz, Yonatan, Lanari, Edoardo: Gray tensor products and Lax functors of (\infty,2)-categories. Adv. Math., Vol. 391, Paper No. 107986, 32, https://doi.org/10.1016/j.aim.2021.107986, DOI:10.1016/j.aim.2021.107986 DOI 10.1016/j.aim.2021.107986 | MR 4305242
[5] Gray, John W.: Formal category theory: Adjointness for 2-categories. Lecture notes in mathematics, vol. 391, Springer-Verlag, Berlin-New York
[6] Joyal, André: The theory of quasi-categories and its applications. Preprint available at http://mat.uab.cat/~kock/crm/hocat/advanced-course/Quadern45-2.pdf
[7] Joyal, André, Tierney, Myles: Quasi-categories vs Segal spaces. Categories in algebra, geometry and mathematical physics, pages 277-326, Contemp. math. 431 MR 2342834
[8] Lack, Stephen: Icons. Appl. Categ. Structures, Vol. 18, Iss. 3, 289-307, https://doi.org/10.1007/s10485-008-9136-5, DOI:10.1007/s10485-008-9136-5 DOI 10.1007/s10485-008-9136-5
[9] Lurie, Jacob: Higher topos theory. Annals of mathematics studies, Princeton University Press, Princeton, NJ, http://dx.doi.org/10.1515/9781400830558, ISBN:978-0-691-14049-0; 0-691-14049-9, DOI:10.1515/9781400830558 DOI 10.1515/9781400830558 | MR 2522659
[10] Ozornova, Viktoriya, Rovelli, Martina: Model structures for (\infty,n)-categories on (pre)stratified simplicial sets and prestratified simplicial spaces. Algebr. Geom. Topol., Vol. 20, Iss. 3, 1543-1600, https://doi.org/10.2140/agt.2020.20.1543, DOI:10.2140/agt.2020.20.1543 DOI 10.2140/agt.2020.20.1543 | MR 4105558
[11] Ozornova, Viktoriya, Rovelli, Martina: Fundamental pushouts of n-complicial sets. High. Struct., Vol. 6, Iss. 1, 403-438, https://doi.org/10.2140/akt.2021.6.97, DOI:10.2140/akt.2021.6.97 DOI 10.2140/akt.2021.6.97 | MR 4456600
[12] Riehl, Emily: Complicial sets, an overture. 2016 MATRIX annals, pages 49-76, MATRIX book ser. 1 MR 3792516
[13] Riehl, Emily, Verity, Dominic: Elements of \infty-category theory. Cambridge studies in advanced mathematics, Cambridge University Press, Cambridge, https://doi.org/10.1017/9781108936880, ISBN:978-1-108-83798-9, DOI:10.1017/9781108936880 DOI 10.1017/9781108936880 | MR 4354541
[14] Verity, Dominic: Complicial sets characterising the simplicial nerves of strict \omega-categories. Mem. Amer. Math. Soc., Vol. 193, Iss. 905, xvi+184, https://doi.org/10.1090/memo/0905, DOI:10.1090/memo/0905 DOI 10.1090/memo/0905 | MR 2399898
[15] Verity, Dominic: Weak complicial sets. I. Basic homotopy theory. Adv. Math., Vol. 219, Iss. 4, 1081-1149, http://dx.doi.org/10.1016/j.aim.2008.06.003, DOI:10.1016/j.aim.2008.06.003 DOI 10.1016/j.aim.2008.06.003 | MR 2450607
Partner of
EuDML logo