Volume 15, issue 5 (2015)

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

Volume 25, 1 issue

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
Editorial Board
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN 1472-2739 (online)
ISSN 1472-2747 (print)
Author Index
To Appear
 
Other MSP Journals
Duality and small functors

Georg Biedermann and Boris Chorny

Algebraic & Geometric Topology 15 (2015) 2609–2657
Bibliography
1 J F Adams, A variant of E H Brown's representability theorem, Topology 10 (1971) 185 MR0283788
2 G Biedermann, B Chorny, O Röndigs, Calculus of functors and model categories, Adv. Math. 214 (2007) 92 MR2348024
3 F Borceux, Handbook of categorical algebra, 2: Categories and structures, Encycl. Math. Appl. 51, Cambridge Univ. Press (1994) MR1313497
4 A K Bousfield, On the telescopic homotopy theory of spaces, Trans. Amer. Math. Soc. 353 (2001) 2391 MR1814075
5 A K Bousfield, E M Friedlander, Homotopy theory of $\Gamma $–spaces, spectra, and bisimplicial sets, from: "Geometric applications of homotopy theory, II", Lecture Notes in Math. 658, Springer (1978) 80 MR513569
6 E H Brown Jr., Cohomology theories, Ann. of Math. 75 (1962) 467 MR0138104
7 B Chorny, A classification of small homotopy functors from spectra to spectra, arXiv:1303.7108
8 B Chorny, A generalization of Quillen's small object argument, J. Pure Appl. Algebra 204 (2006) 568 MR2185618
9 B Chorny, Brown representability for space-valued functors, Israel J. Math. 194 (2013) 767 MR3047091
10 B Chorny, W G Dwyer, Homotopy theory of small diagrams over large categories, Forum Math. 21 (2009) 167 MR2503302
11 B Chorny, J Rosický, Class-combinatorial model categories, Homology Homotopy Appl. 14 (2012) 263 MR2954676
12 B Chorny, J Rosický, Class-locally presentable and class-accessible categories, J. Pure Appl. Algebra 216 (2012) 2113 MR2925805
13 J D Christensen, D C Isaksen, Duality and pro-spectra, Algebr. Geom. Topol. 4 (2004) 781 MR2100680
14 B Day, On closed categories of functors, from: "Reports of the Midwest Category Seminar, IV", Lecture Notes in Mathematics 137, Springer (1970) 1 MR0272852
15 B J Day, S Lack, Limits of small functors, J. Pure Appl. Algebra 210 (2007) 651 MR2324597
16 A Dold, D Puppe, Duality, trace, and transfer, from: "Proceedings of the International Conference on Geometric Topology" (editor K Borsuk), PWN (1980) 81 MR656721
17 D Dugger, Combinatorial model categories have presentations, Adv. Math. 164 (2001) 177 MR1870516
18 B I Dundas, O Röndigs, P A Østvær, Enriched functors and stable homotopy theory, Doc. Math. 8 (2003) 409 MR2029170
19 A D Elmendorf, I Kriz, M A Mandell, J P May, Rings, modules, and algebras in stable homotopy theory, Mathematical Surveys and Monographs 47, Amer. Math. Soc. (1997) MR1417719
20 P J Freyd, Abelian categories, Harper and Row (1964)
21 P Freyd, Several new concepts: Lucid and concordant functors, pre-limits, pre-completeness, the continuous and concordant completions of categories, from: "Category Theory, Homology Theory and their Applications, III", Springer (1969) 196 MR0246929
22 T G Goodwillie, Calculus, III: Taylor series, Geom. Topol. 7 (2003) 645 MR2026544
23 P S Hirschhorn, Model categories and their localizations, Mathematical Surveys and Monographs 99, Amer. Math. Soc. (2003) MR1944041
24 M Hovey, B Shipley, J Smith, Symmetric spectra, J. Amer. Math. Soc. 13 (2000) 149 MR1695653
25 J F Jardine, Representability theorems for presheaves of spectra, J. Pure Appl. Algebra 215 (2011) 77 MR2678701
26 G M Kelly, Basic concepts of enriched category theory, London Math. Soc. Lecture Notes 64, Cambridge Univ. Press (1982) 245 MR651714
27 J Lurie, Higher topos theory, Annals of Mathematics Studies 170, Princeton Univ. Press (2009) MR2522659
28 M Lydakis, Simplicial functors and stable homotopy theory, preprint (1998)
29 M Makkai, R Paré, Accessible categories: The foundations of categorical model theory, Contemporary Mathematics 104, Amer. Math. Soc. (1989) MR1031717
30 A Neeman, Brown representability for the dual, Invent. Math. 133 (1998) 97 MR1626473
31 S Schwede, B E Shipley, Algebras and modules in monoidal model categories, Proc. London Math. Soc. 80 (2000) 491 MR1734325
32 W C Waterhouse, Basically bounded functors and flat sheaves, Pacific J. Math. 57 (1975) 597 MR0396578
33 G W Whitehead, Generalized homology theories, Trans. Amer. Math. Soc. 102 (1962) 227 MR0137117