Algebraic & Geometric Topology Volume 24, issue 3 (2024)

Download this article
	For screen
	For printing

Recent 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

Models of $G$–spectra as presheaves of spectra

Bertrand J Guillou and J Peter May

Algebraic & Geometric Topology 24 (2024) 1225–1275

DOI: 10.2140/agt.2024.24.1225

Bibliography

1	G Arone, I Barnea, T M Schlank, Noncommutative CW–spectra as enriched presheaves on matrix algebras, J. Noncommut. Geom. 16 (2022) 1411 MR4542390
2	C Barwick, Spectral Mackey functors and equivariant algebraic K–theory, I, Adv. Math. 304 (2017) 646 MR3558219
3	C Barwick, S Glasman, J Shah, Spectral Mackey functors and equivariant algebraic K–theory, II, Tunis. J. Math. 2 (2020) 97 MR3933393
4	A M Bohmann, A Osorno, Constructing equivariant spectra via categorical Mackey functors, Algebr. Geom. Topol. 15 (2015) 537 MR3325747
5	M Bökstedt, W C Hsiang, I Madsen, The cyclotomic trace and algebraic K–theory of spaces, Invent. Math. 111 (1993) 465 MR1202133
6	G Carlsson, Equivariant stable homotopy and Segal’s Burnside ring conjecture, Ann. of Math. 120 (1984) 189 MR0763905
7	G Carlsson, A survey of equivariant stable homotopy theory, Topology 31 (1992) 1 MR1153236
8	D Clausen, A Mathew, N Naumann, J Noel, Descent and vanishing in chromatic algebraic K–theory via group actions, (2020) arXiv:2011.08233
9	S R Costenoble, S Waner, Fixed set systems of equivariant infinite loop spaces, Trans. Amer. Math. Soc. 326 (1991) 485 MR1012523
10	G Dunn, E_n–monoidal categories and their group completions, J. Pure Appl. Algebra 95 (1994) 27 MR1289117
11	A D Elmendorf, M A Mandell, Permutative categories, multicategories and algebraic K–theory, Algebr. Geom. Topol. 9 (2009) 2391 MR2558315
12	A D Elmendorf, L G Lewis Jr., J P May, Brave new equivariant foundations, from: "Equivariant homotopy and cohomology theory" (editor J P May), CBMS Reg. Conf. Ser. Math. 91, Amer. Math. Soc. (1996) 283 MR1413302
13	A D Elmendorf, I Kriz, M A Mandell, J P May, Rings, modules, and algebras in stable homotopy theory, 47, Amer. Math. Soc. (1997) MR1417719
14	J P C Greenlees, J P May, Equivariant stable homotopy theory, from: "Handbook of algebraic topology" (editor I M James), North-Holland (1995) 277 MR1361893
15	J P C Greenlees, J P May, Generalized Tate cohomology, 543, Amer. Math. Soc. (1995) MR1230773
16	J P C Greenlees, J P May, Localization and completion theorems for MU–module spectra, Ann. of Math. 146 (1997) 509 MR1491447
17	B J Guillou, Strictification of categories weakly enriched in symmetric monoidal categories, Theory Appl. Categ. 24 (2010) 564 MR2770075
18	B J Guillou, J P May, Equivariant iterated loop space theory and permutative G–categories, Algebr. Geom. Topol. 17 (2017) 3259 MR3709647
19	B J Guillou, J P May, Enriched model categories and presheaf categories, New York J. Math. 26 (2020) 37 MR4047399
20	B J Guillou, J P May, M Merling, Categorical models for equivariant classifying spaces, Algebr. Geom. Topol. 17 (2017) 2565 MR3704236
21	B Guillou, J P May, M Merling, A M Osorno, A symmetric monoidal and equivariant Segal infinite loop space machine, J. Pure Appl. Algebra 223 (2019) 2425 MR3906557
22	B J Guillou, J P May, M Merling, A M Osorno, Symmetric monoidal G–categories and their strictification, Q. J. Math. 71 (2020) 207 MR4077192
23	B J Guillou, J P May, M Merling, A M Osorno, Multiplicative equivariant K–theory and the Barratt–Priddy–Quillen theorem, Adv. Math. 414 (2023) 108865 MR4540921
24	M A Hill, M J Hopkins, D C Ravenel, On the nonexistence of elements of Kervaire invariant one, Ann. of Math. 184 (2016) 1 MR3505179
25	M Hyland, J Power, Pseudo-commutative monads and pseudo-closed 2–categories, J. Pure Appl. Algebra 175 (2002) 141 MR1935977
26	T A Kro, Model structure on operads in orthogonal spectra, Homology Homotopy Appl. 9 (2007) 397 MR2366955
27	L G Lewis Jr., Is there a convenient category of spectra?, J. Pure Appl. Algebra 73 (1991) 233 MR1124786
28	L G Lewis Jr., J P May, Equivariant duality theory, from: "Equivariant stable homotopy theory" (editors A Dold, B Eckmann), Lecture Notes in Math. 1213, Springer (1986) 117 MR0866482
29	L G Lewis Jr., J P May, The equivariant stable category, from: "Equivariant stable homotopy theory" (editors A Dold, B Eckmann), Lecture Notes in Math. 1213, Springer (1986) 6 MR0866482
30	L G Lewis Jr., J P May, Equivariant transfer, from: "Equivariant stable homotopy theory" (editors A Dold, B Eckmann), Lecture Notes in Math. 1213, Springer (1986) 175 MR0866482
31	L G Lewis Jr., J P May, J E McClure, The Burnside ring and splittings in equivariant homology theory, from: "Equivariant stable homotopy theory" (editors A Dold, B Eckmann), Lecture Notes in Math. 1213, Springer (1986) 236 MR0866482
32	L G Lewis Jr., J P May, M Steinberger, J E McClure, Equivariant stable homotopy theory, 1213, Springer (1986) MR0866482
33	J A Lind, Diagram spaces, diagram spectra and spectra of units, Algebr. Geom. Topol. 13 (2013) 1857 MR3073903
34	C Malkiewich, M Merling, Equivariant A–theory, Doc. Math. 24 (2019) 815 MR3982285
35	C Malkiewich, M Merling, The equivariant parametrized h–cobordism theorem, the non-manifold part, Adv. Math. 399 (2022) 108242 MR4384608
36	M A Mandell, J P May, Equivariant orthogonal spectra and S–modules, 755, Amer. Math. Soc. (2002) MR1922205
37	M A Mandell, J P May, S Schwede, B Shipley, Model categories of diagram spectra, Proc. Lond. Math. Soc. 82 (2001) 441 MR1806878
38	J P May, The geometry of iterated loop spaces, 271, Springer (1972) MR0420610
39	J P May, E_∞ spaces, group completions, and permutative categories, from: "New developments in topology" (editor G Segal), Lond. Math. Soc. Lect. Note Ser. 11, Cambridge Univ. Press (1974) 61 MR0339152
40	J P May, E_∞ ring spaces and E_∞ ring spectra, 577, Springer (1977) 268 MR0494077
41	J P May, The spectra associated to permutative categories, Topology 17 (1978) 225 MR0508886
42	J P May, Pairings of categories and spectra, J. Pure Appl. Algebra 19 (1980) 299 MR0593258
43	J P May, Equivariant homotopy and cohomology theory, 91, Amer. Math. Soc. (1996) MR1413302
44	J P May, What precisely are E_∞ ring spaces and E_∞ ring spectra ?, from: "New topological contexts for Galois theory and algebraic geometry" (editors A Baker, B Richter), Geom. Topol. Monogr. 16, Geom. Topol. Publ. (2009) 215 MR2544391
45	J P May, M Merling, A M Osorno, Equivariant infinite loop space theory, the space level story, (2017) arXiv:1704.03413
46	D Nardin, Parametrized higher category theory and higher algebra, IV : Stability with respect to an orbital ∞–category, preprint (2016) arXiv:1608.07704
47	R J Piacenza, The homotopy theory of diagrams, from: "Equivariant homotopy and cohomology theory" (editor J P May), CBMS Reg. Conf. Ser. Math. 91, Amer. Math. Soc. (1996) 47 MR1413302
48	K Ponto, M Shulman, Duality and traces for indexed monoidal categories, Theory Appl. Categ. 26 (2012) 582 MR3065938
49	S Sagave, C Schlichtkrull, Diagram spaces and symmetric spectra, Adv. Math. 231 (2012) 2116 MR2964635
50	V Schmitt, Tensor product for symmetric monoidal categories, preprint (2007) arXiv:0711.0324
51	S Schwede, B Shipley, Stable model categories are categories of modules, Topology 42 (2003) 103 MR1928647
52	K Shimakawa, Infinite loop G–spaces associated to monoidal G–graded categories, Publ. Res. Inst. Math. Sci. 25 (1989) 239 MR1003787