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

Volume 26
Issue 5, 1597–1963
Issue 4, 1229–1596
Issue 3, 825–1227
Issue 2, 411–824
Issue 1, 1–410

Volume 25, 9 issues

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
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
 
Subscriptions
 
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
 
Author index
To appear
 
Other MSP journals
Presheaves of groupoids as models for homotopy types

Léonard Guetta

Algebraic & Geometric Topology 25 (2025) 3833–3874
Bibliography
1 D Ara, D C Cisinski, I Moerdijk, The dendroidal category is a test category, Math. Proc. Cambridge Philos. Soc. 167 (2019) 107 MR3968823
2 C Barwick, D M Kan, A characterization of simplicial localization functors and a discussion of DK equivalences, Indag. Math. 23 (2012) 69 MR2877402
3 D C Cisinski, Le localisateur fondamental minimal, Cah. Topol. Géom. Différ. Catég. 45 (2004) 109 MR2072934
4 D C Cisinski, Les préfaisceaux comme modèles des types d’homotopie, 308, Soc. Math. France (2006) MR2294028
5 D C Cisinski, G Maltsiniotis, La catégorie Θ de Joyal est une catégorie test, J. Pure Appl. Algebra 215 (2011) 962 MR2747231
6 S E Crans, Quillen closed model structures for sheaves, J. Pure Appl. Algebra 101 (1995) 35 MR1346427
7 A Dold, Homology of symmetric products and other functors of complexes, Ann. of Math. 68 (1958) 54 MR97057
8 P Gabriel, M Zisman, Calculus of fractions and homotopy theory, 35, Springer (1967) MR210125
9 J W Gray, The categorical comprehension scheme, from: "Category theory, homology theory and their applications, III", Lecture Notes in Math. 99, Springer (1969) 242 MR249483
10 A Grothendieck, Pursuing stacks (À la poursuite des champs), I, 20, Soc. Math. France (2022) MR4468847
11 L Illusie, Complexe cotangent et déformations, II, 283, Springer (1972) MR491681
12 A Joyal, M Tierney, On the homotopy theory of sheaves of simplicial groupoids, Math. Proc. Cambridge Philos. Soc. 120 (1996) 263 MR1384469
13 D M Kan, Functors involving c.s.s. complexes, Trans. Amer. Math. Soc. 87 (1958) 330 MR131873
14 D M Kan, On homotopy theory and c.s.s. groups, Ann. of Math. 68 (1958) 38 MR111033
15 J L Loday, Spaces with finitely many nontrivial homotopy groups, J. Pure Appl. Algebra 24 (1982) 179 MR651845
16 S MacLane, J H C Whitehead, On the 3-type of a complex, Proc. Nat. Acad. Sci. U.S.A. 36 (1950) 41 MR33519
17 G Maltsiniotis, La théorie de l’homotopie de Grothendieck, 301, Soc. Math. France (2005) MR2200690
18 G Maltsiniotis, La catégorie cubique avec connexions est une catégorie test stricte, Homology Homotopy Appl. 11 (2009) 309 MR2591923
19 J Milnor, The geometric realization of a semi-simplicial complex, Ann. of Math. 65 (1957) 357 MR84138
20 R Street, Limits indexed by category-valued 2-functors, J. Pure Appl. Algebra 8 (1976) 149 MR401868
21 R W Thomason, Homotopy colimits in the category of small categories, Math. Proc. Cambridge Philos. Soc. 85 (1979) 91 MR510404
22 A P Tonks, Cubical groups which are Kan, J. Pure Appl. Algebra 81 (1992) 83 MR1173825