Download this article
 Download this article For screen
For printing
Recent Issues

Volume 25
Issue 3, 1265–1915
Issue 2, 645–1264
Issue 1, 1–644

Volume 24, 9 issues

Volume 23, 9 issues

Volume 22, 8 issues

Volume 21, 7 issues

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN 1472-2739 (online)
ISSN 1472-2747 (print)
Author Index
To Appear
 
Other MSP Journals
Rigidification of cubical quasicategories

Pierre-Louis Curien, Muriel Livernet and Gabriel Saadia

Algebraic & Geometric Topology 24 (2024) 2851–2888
Bibliography
1 H J Baues, Geometry of loop spaces and the cobar construction, 230, Amer. Math. Soc. (1980) MR0567799
2 J E Bergner, The homotopy theory of (,1)–categories, 90, Cambridge Univ. Press (2018) MR3791455
3 A Björner, Orderings of Coxeter groups, from: "Combinatorics and algebra" (editor C Greene), Contemp. Math. 34, Amer. Math. Soc. (1984) 175 MR0777701
4 J M Boardman, R M Vogt, Homotopy invariant algebraic structures on topological spaces, 347, Springer (1973) MR0420609
5 D C Cisinski, Univalent universes for elegant models of homotopy types, preprint (2014) arXiv:1406.0058
6 C Cohen, T Coquand, S Huber, A Mörtberg, Cubical type theory: a constructive interpretation of the univalence axiom, from: "21st international conference on types for proofs and programs" (editor T Uustalu), Leibniz Int. Proc. Inform. 69, Schloss Dagstuhl (2018) 5 MR3781068
7 B Doherty, K Kapulkin, Z Lindsey, C Sattler, Cubical models of (,1)–categories, 1484, Amer. Math. Soc. (2024) MR4756398
8 D Dugger, D I Spivak, Rigidification of quasi-categories, Algebr. Geom. Topol. 11 (2011) 225 MR2764042
9 D Dugger, D I Spivak, Mapping spaces in quasi-categories, Algebr. Geom. Topol. 11 (2011) 263 MR2764043
10 L Fajstrup, E Goubault, E Haucourt, S Mimram, M Raussen, Directed algebraic topology and concurrency, Springer (2016) MR3445318
11 P Gaucher, Towards a homotopy theory of process algebra, Homology Homotopy Appl. 10 (2008) 353 MR2426108
12 M Grandis, L Mauri, Cubical sets and their site, Theory Appl. Categ. 11 (2003) 185 MR1988396
13 P S Hirschhorn, Model categories and their localizations, 99, Amer. Math. Soc. (2003) MR1944041
14 A Joyal, Quasi-categories vs simplicial categories, unpublished manuscript (2007)
15 A Joyal, The theory of quasi-categories and its applications, II, lecture notes (2008)
16 K Kapulkin, Z Lindsey, L Z Wong, A co-reflection of cubical sets into simplicial sets with applications to model structures, New York J. Math. 25 (2019) 627 MR3992314
17 J Lurie, Higher topos theory, 170, Princeton Univ. Press (2009) MR2522659
18 S Mac Lane, Categories for the working mathematician, 5, Springer (1998) MR1712872
19 G Maltsiniotis, La catégorie cubique avec connexions est une catégorie test stricte, Homology Homotopy Appl. 11 (2009) 309 MR2591923
20 V Pratt, Modeling concurrency with geometry, from: "Proceedings of the 18th ACM SIGPLAN-SIGACT symposium on principles of programming languages", Association for Computing Machinery (1991) 311
21 E Riehl, Categorical homotopy theory, 24, Cambridge Univ. Press (2014) MR3221774
22 J P Serre, Homologie singulière des espaces fibrés : applications, Ann. of Math. 54 (1951) 425 MR0045386
23 L Z Wong, Cubes with connections from algebraic weak factorization systems, presentation slides (2020)
24 G M Ziegler, Lectures on polytopes, 152, Springer (1995) MR1311028
25 K Ziemiański, Spaces of directed paths on pre-cubical sets, Appl. Algebra Engrg. Comm. Comput. 28 (2017) 497 MR3722069
26 K Ziemiański, Spaces of directed paths on pre-cubical sets, II, J. Appl. Comput. Topol. 4 (2020) 45 MR4070250