Geometry & Topology Volume 29, issue 3 (2025)

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ISSN (electronic): 1364-0380

ISSN (print): 1465-3060

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Global homotopy theory via partially lax limits

Sil Linskens, Denis Nardin and Luca Pol

Geometry & Topology 29 (2025) 1345–1440

DOI: 10.2140/gt.2025.29.1345

Bibliography

1	D Ayala, J Francis, Fibrations of ∞-categories, High. Struct. 4 (2020) 168 MR4074276
2	T Bachmann, M Hoyois, Norms in motivic homotopy theory, 425, Soc. Math. France (2021) MR4288071
3	I Barnea, Y Harpaz, G Horel, Pro-categories in homotopy theory, Algebr. Geom. Topol. 17 (2017) 567 MR3604386
4	C Barwick, Spectral Mackey functors and equivariant algebraic K-theory, I, Adv. Math. 304 (2017) 646 MR3558219
5	S Ben-Moshe, T M Schlank, Higher semiadditive algebraic K-theory and redshift, Compos. Math. 160 (2024) 237 MR4679205
6	J D Berman, On lax limits in ∞-categories, Proc. Amer. Math. Soc. 152 (2024) 5055 MR4855870
7	A M Bohmann, Global orthogonal spectra, Homology Homotopy Appl. 16 (2014) 313 MR3217308
8	D C Cisinski, Higher categories and homotopical algebra, 180, Cambridge Univ. Press (2019) MR3931682
9	D Degrijse, M Hausmann, W Lück, I Patchkoria, S Schwede, Proper equivariant stable homotopy theory, 1432, Amer. Math. Soc. (2023) MR4627088
10	B Drew, M Gallauer, The universal six-functor formalism, Ann. K-Theory 7 (2022) 599 MR4560376
11	A D Elmendorf, Systems of fixed point sets, Trans. Amer. Math. Soc. 277 (1983) 275 MR690052
12	D Gepner, A Henriques, Homotopy theory of orbispaces, preprint (2007) arXiv:math/0701916
13	D Gepner, L Meier, On equivariant topological modular forms, Compos. Math. 159 (2023) 2638 MR4664814
14	D Gepner, R Haugseng, T Nikolaus, Lax colimits and free fibrations in ∞-categories, Doc. Math. 22 (2017) 1225 MR3690268
15	S Glasman, A note on commutative algebras and their modules in quasicategories, preprint (2014) arXiv:1409.3506
16	S Glasman, Day convolution for ∞-categories, Math. Res. Lett. 23 (2016) 1369 MR3601070
17	J P C Greenlees, J P May, Localization and completion theorems for MU-module spectra, Ann. of Math. 146 (1997) 509 MR1491447
18	M Hausmann, Symmetric spectra model global homotopy theory of finite groups, Algebr. Geom. Topol. 19 (2019) 1413 MR3954287
19	M Hausmann, Global group laws and equivariant bordism rings, Ann. of Math. 195 (2022) 841 MR4413745
20	V Hinich, Rectification of algebras and modules, Doc. Math. 20 (2015) 879 MR3404213
21	V Hinich, Dwyer–Kan localization revisited, Homology Homotopy Appl. 18 (2016) 27 MR3460765
22	M Hovey, Model categories, 63, Amer. Math. Soc. (1999) MR1650134
23	A Joyal, The theory of quasi-categories and its applications, preprint (2008)
24	B Juran, Orbifolds, orbispaces and global homotopy theory, preprint (2020) arXiv:2006.12374
25	A Körschgen, A comparison of two models of orbispaces, Homology Homotopy Appl. 20 (2018) 329 MR3775363
26	T Lenz, Global algebraic K-theory is Swan K-theory, preprint (2022) arXiv:2202.07272
27	T Lenz, G-global homotopy theory and algebraic K-theory, 1545, Amer. Math. Soc. (2025) MR4865560
28	L G Lewis Jr., J P May, M Steinberger, J E McClure, Equivariant stable homotopy theory, 1213, Springer (1986) MR866482
29	J Lurie, Higher topos theory, 170, Princeton Univ. Press (2009) MR2522659
30	J Lurie, Higher algebra, preprint (2017)
31	M A Mandell, J P May, Equivariant orthogonal spectra and S-modules, 755, Amer. Math. Soc. (2002) MR1922205
32	H K Nguyen, G Raptis, C Schrade, Adjoint functor theorems for ∞-categories, J. Lond. Math. Soc. 101 (2020) 659 MR4093970
33	C Rezk, Global homotopy theory and cohesion, preprint (2014)
34	E Riehl, D Verity, Homotopy coherent adjunctions and the formal theory of monads, Adv. Math. 286 (2016) 802 MR3415698
35	S Schwede, Equivariant properties of symmetric products, J. Amer. Math. Soc. 30 (2017) 673 MR3630085
36	S Schwede, Global homotopy theory, 34, Cambridge Univ. Press (2018) MR3838307
37	S Schwede, Orbispaces, orthogonal spaces, and the universal compact Lie group, Math. Z. 294 (2020) 71 MR4050064
38	S Schwede, B E Shipley, Algebras and modules in monoidal model categories, Proc. Lond. Math. Soc. 80 (2000) 491 MR1734325
39	J Shah, Parametrized higher category theory, II: Universal constructions, preprint (2021) arXiv:2109.11954
40	J Shah, Parametrized higher category theory, Algebr. Geom. Topol. 23 (2023) 509 MR4587313
41	M Stephan, On equivariant homotopy theory for model categories, Homology Homotopy Appl. 18 (2016) 183 MR3551501