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External Spanier–Whitehead duality and homology representation theorems for diagram spaces

Malte Lackmann

Algebraic & Geometric Topology 23 (2023) 155–216
Bibliography
1 N Bárcenas, Brown representability and spaces over a category, Rev. Colombiana Mat. 48 (2014) 55 MR3230797
2 A Bartels, M Bestvina, The Farrell–Jones conjecture for mapping class groups, Invent. Math. 215 (2019) 651 MR3910072
3 A Bartels, W Lück, The Borel conjecture for hyperbolic and CAT(0)–groups, Ann. of Math. 175 (2012) 631 MR2993750
4 A Bartels, W Lück, H Reich, The K–theoretic Farrell–Jones conjecture for hyperbolic groups, Invent. Math. 172 (2008) 29 MR2385666
5 J Bénabou, Les distributeurs : d’après le cours de questions spéciales de mathématique, rapport (1973)
6 F Borceux, Handbook of categorical algebra, I: Basic category theory, 50, Cambridge Univ. Press (1994) MR1291599
7 F Borceux, Handbook of categorical algebra, II: Categories and structures, 51, Cambridge Univ. Press (1994) MR1313497
8 E H Brown Jr., Cohomology theories, Ann. of Math. 75 (1962) 467 MR138104
9 W Casselman, Introduction to the theory of admissible representations of p–adic reductive groups, (1995)
10 J F Davis, W Lück, Spaces over a category and assembly maps in isomorphism conjectures in K– and L–theory, K–Theory 15 (1998) 201 MR1659969
11 D Degrijse, M Hausmann, W Lück, I Patchkoria, S Schwede, Proper equivariant stable homotopy theory, preprint (2019) arXiv:1908.00779
12 W G Dwyer, J Spaliński, Homotopy theories and model categories, from: "Handbook of algebraic topology" (editor I M James), North-Holland (1995) 73 MR1361887
13 A D Elmendorf, Systems of fixed point sets, Trans. Amer. Math. Soc. 277 (1983) 275 MR690052
14 P G Goerss, J F Jardine, Simplicial homotopy theory, Birkhäuser (2009) MR2840650
15 K R Goodearl, von Neumann regular rings, Krieger (1991) MR1150975
16 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
17 P S Hirschhorn, Model categories and their localizations, 99, Amer. Math. Soc. (2003) MR1944041
18 J Hollender, R M Vogt, Modules of topological spaces, applications to homotopy limits and E structures, Arch. Math. (Basel) 59 (1992) 115 MR1170635
19 M Hovey, Model categories, 63, Amer. Math. Soc. (1999) MR1650134
20 M Hovey, Model category structures on chain complexes of sheaves, Trans. Amer. Math. Soc. 353 (2001) 2441 MR1814077
21 M Hovey, Spectra and symmetric spectra in general model categories, J. Pure Appl. Algebra 165 (2001) 63 MR1860878
22 M Hovey, B Shipley, J Smith, Symmetric spectra, J. Amer. Math. Soc. 13 (2000) 149 MR1695653
23 L Illusie, Frobenius and Hodge degeneration, from: "Introduction to Hodge theory", SMF/AMS Texts and Monographs 8, Amer. Math. Soc. (2002) 99 MR1924513
24 H Kammeyer, W Lück, H Rüping, The Farrell–Jones conjecture for arbitrary lattices in virtually connected Lie groups, Geom. Topol. 20 (2016) 1275 MR3523058
25 D Kasprowski, M Ullmann, C Wegner, C Winges, The A–theoretic Farrell–Jones conjecture for virtually solvable groups, Bull. Lond. Math. Soc. 50 (2018) 219 MR3830115
26 H Krause, Derived categories, resolutions, and Brown representability, from: "Interactions between homotopy theory and algebra" (editors L L Avramov, J D Christensen, W G Dwyer, M A Mandell, B E Shipley), Contemp. Math. 436, Amer. Math. Soc. (2007) 101 MR2355771
27 M Lackmann, Equivariant (co-)homology for infinite groups, master’s thesis, University of Bonn (2016)
28 M Lackmann, External Spanier–Whitehead duality for 𝒞–spectra and applications to 𝒞–homology theories, PhD thesis, University of Bonn (2021)
29 M Lackmann, L Li, Sufficient and necessary conditions for hereditarity of infinite category algebras, J. Algebra 602 (2022) 322 MR4404525
30 L G Lewis Jr., J P May, M Steinberger, J E McClure, Equivariant stable homotopy theory, 1213, Springer (1986) MR866482
31 L Li, A characterization of finite EI categories with hereditary category algebras, J. Algebra 345 (2011) 213 MR2842063
32 W Lück, Chern characters for proper equivariant homology theories and applications to K– and L–theory, J. Reine Angew. Math. 543 (2002) 193 MR1887884
33 W Lück, H Reich, The Baum–Connes and the Farrell–Jones conjectures in K– and L–theory, from: "Handbook of K–theory, II" (editors E M Friedlander, D R Grayson), Springer (2005) 703 MR2181833
34 A T Lundell, S Weingram, The topology of CW complexes, Van Nostrand Reinhold (1969) MR3822092
35 S Mac Lane, Homology, 114, Springer (1963) MR0156879
36 M A Mandell, J P May, S Schwede, B Shipley, Model categories of diagram spectra, Proc. London Math. Soc. 82 (2001) 441 MR1806878
37 J P May, Equivariant homotopy and cohomology theory, 91, Amer. Math. Soc. (1996) MR1413302
38 J P May, J Sigurdsson, Parametrized homotopy theory, 132, Amer. Math. Soc. (2006) MR2271789
39 J S Milne, Algebraic groups: the theory of group schemes of finite type over a field, 170, Cambridge Univ. Press (2017) MR3729270
40 B Mitchell, Rings with several objects, Advances in Math. 8 (1972) 1 MR294454
41 A Neeman, On a theorem of Brown and Adams, Topology 36 (1997) 619 MR1422428
42 A Neeman, Triangulated categories, 148, Princeton Univ. Press (2001) MR1812507
43 D G Quillen, Homotopical algebra, 43, Springer (1967) MR0223432
44 J J Rotman, An introduction to homological algebra, 85, Academic (1979) MR538169
45 H Rüping, The Farrell–Jones conjecture for S–arithmetic groups, J. Topol. 9 (2016) 51 MR3465840
46 S Schwede, Global homotopy theory, 34, Cambridge Univ. Press (2018) MR3838307
47 S Schwede, B E Shipley, Algebras and modules in monoidal model categories, Proc. London Math. Soc. 80 (2000) 491 MR1734325
48 S Schwede, B Shipley, Equivalences of monoidal model categories, Algebr. Geom. Topol. 3 (2003) 287 MR1997322
49 S Schwede, B Shipley, Stable model categories are categories of modules, Topology 42 (2003) 103 MR1928647
50 B Shipley, H–algebra spectra are differential graded algebras, Amer. J. Math. 129 (2007) 351 MR2306038
51 M Shulman, Homotopy limits and colimits and enriched homotopy theory, preprint (2006) arXiv:math/0610194
52 M Shulman, Enriched indexed categories, Theory Appl. Categ. 28 (2013) 616 MR3094435
53 D Simson, A remark on projective dimension of flat modules, Math. Ann. 209 (1974) 181 MR344292
54 M Stephan, On equivariant homotopy theory for model categories, Homology Homotopy Appl. 18 (2016) 183 MR3551501
55 J Thévenaz, P J Webb, Simple Mackey functors, from: "Proceedings of the Second International Group Theory Conference" (1990) 299 MR1068370
56 J Thévenaz, P Webb, The structure of Mackey functors, Trans. Amer. Math. Soc. 347 (1995) 1865 MR1261590
57 G V Triantafillou, Rationalization for Hopf G–spaces, Math. Z. 182 (1983) 485 MR701365
58 O Y Viro, D B Fuchs, Homology and cohomology, from: "Topology, II" (editors S P Novikov, V A Rokhlin), Encyclopaedia Math. Sci. 24, Springer (2004) 95 MR2054457
59 C Wegner, The Farrell–Jones conjecture for virtually solvable groups, J. Topol. 8 (2015) 975 MR3431666
60 X Wu, Farrell–Jones conjecture for fundamental groups of graphs of virtually cyclic groups, Topology Appl. 206 (2016) 185 MR3494441
61 F Xu, Homological properties of category algebras, PhD thesis, University of Minnesota (2006)