Volume 17, issue 1 (2017)

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Pro-categories in homotopy theory

Ilan Barnea, Yonatan Harpaz and Geoffroy Horel

Algebraic & Geometric Topology 17 (2017) 567–643
Bibliography
1 J Adámek, J Rosický, Locally presentable and accessible categories, 189, Cambridge University Press (1994) MR1294136
2 D W Anderson, Fibrations and geometric realizations, Bull. Amer. Math. Soc. 84 (1978) 765 MR0500935
3 M Artin, A Grothendieck, J L Verdier, Théorie des topos et cohomologie étale des schémas, Tome 1 : Théorie des topos, Exposés I–IV (SGA 41), 269, Springer (1972) MR0354652
4 M Artin, B Mazur, Etale homotopy, 100, Springer (1969) MR0245577
5 I Barnea, M Joachim, S Mahanta, Model structure on projective systems of C–algebras and bivariant homology theories, (2015) arXiv:1508.04283
6 I Barnea, T M Schlank, Model structures on ind-categories and the accessibility rank of weak equivalences, Homology Homotopy Appl. 17 (2015) 235 MR3426382
7 I Barnea, T M Schlank, A new model for pro-categories, J. Pure Appl. Algebra 219 (2015) 1175 MR3282132
8 I Barnea, T M Schlank, A projective model structure on pro-simplicial sheaves, and the relative étale homotopy type, Adv. Math. 291 (2016) 784 MR3459031
9 K S Brown, Abstract homotopy theory and generalized sheaf cohomology, Trans. Amer. Math. Soc. 186 (1973) 419 MR0341469
10 D C Cisinski, Catégories dérivables, Bull. Soc. Math. France 138 (2010) 317 MR2729017
11 D C Cisinski, Invariance de la K–théorie par équivalences dérivées, J. K-Theory 6 (2010) 505 MR2746284
12 D Dugger, Combinatorial model categories have presentations, Adv. Math. 164 (2001) 177 MR1870516
13 W G Dwyer, D M Kan, Function complexes in homotopical algebra, Topology 19 (1980) 427 MR584566
14 D A Edwards, H M Hastings, Čech and Steenrod homotopy theories with applications to geometric topology, 542, Springer (1976) MR0428322
15 P G Goerss, J F Jardine, Simplicial homotopy theory, 174, Birkhäuser (1999) MR1711612
16 V Hinich, Dwyer–Kan localization revisited, Homology Homotopy Appl. 18 (2016) 27 MR3460765
17 P S Hirschhorn, Model categories and their localizations, 99, Amer. Math. Soc. (2003) MR1944041
18 G Horel, Profinite completion of operads and the Grothendieck–Teichmüller group, preprint (2015) arXiv:1504.01605
19 G Horel, Brown categories and bicategories, Homology Homotopy Appl. 18 (2016) 217
20 D C Isaksen, A model structure on the category of pro-simplicial sets, Trans. Amer. Math. Soc. 353 (2001) 2805 MR1828474
21 D C Isaksen, Strict model structures for pro-categories, from: "Categorical decomposition techniques in algebraic topology" (editors G Arone, J Hubbuck, R Levi, M Weiss), Progr. Math. 215, Birkhäuser (2004) 179 MR2039766
22 D C Isaksen, Completions of pro-spaces, Math. Z. 250 (2005) 113 MR2136405
23 J F Jardine, Simplicial presheaves, J. Pure Appl. Algebra 47 (1987) 35 MR906403
24 J F Jardine, Fields lectures: simplicial presheaves, lecture notes (2007)
25 A Joyal, letter to Grothendieck (1984)
26 A Joyal, The theory of quasi-categories and its applications, lecture notes (2008)
27 C Kapulkin, K Szumiło, Quasicategories of frames of cofibration categories, preprint (2015) arXiv:1506.08681v1
28 J Lurie, Higher topos theory, 170, Princeton University Press (2009) MR2522659
29 J Lurie, Rational and p–adic homotopy theory, unpublished (2011)
30 J Lurie, Higher algebra, unpublished (2014)
31 A Mazel-Gee, Quillen adjunctions induce adjunctions of quasicategories, New York J. Math. 22 (2016) 57 MR3484677
32 C V Meyer, Approximation filtrante de diagrammes finis par Pro-C, Ann. Sci. Math. Québec 4 (1980) 35 MR574833
33 F Morel, Ensembles profinis simpliciaux et interprétation géométrique du foncteur T, Bull. Soc. Math. France 124 (1996) 347 MR1414543
34 G Quick, Continuous group actions on profinite spaces, J. Pure Appl. Algebra 215 (2011) 1024 MR2747236
35 D G Quillen, Homotopical algebra, 43, Springer (1967) MR0223432
36 A Radlescu-Banu, Cofibrations in homotopy theory, preprint (2006) arXiv:math/0610009
37 H Schubert, Categories, Springer (1972) MR0349793
38 J P Serre, Corps locaux, VIII, Hermann (1962) 243 MR0150130
39 M A Shulman, Set theory for category theory, preprint (2008) arXiv:0810.1279
40 K Szumiło, Two models for the homotopy theory of cocomplete homotopy theories, preprint (2014) arXiv:1411.0303
41 R W Thomason, Homotopy colimits in the category of small categories, Math. Proc. Cambridge Philos. Soc. 85 (1979) 91 MR510404
42 B Toën, G Vezzosi, Segal topoi and stacks over Segal categories, preprint (2002) arXiv:math/0212330