Volume 21, issue 5 (2021)

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

Volume 22
Issue 2, 473–990
Issue 1, 1–472

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
Editorial Interests
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Author Index
To Appear
 
Other MSP Journals
Magnitude homology of enriched categories and metric spaces

Tom Leinster and Michael Shulman

Algebraic & Geometric Topology 21 (2021) 2175–2221
Bibliography
1 Y Asao, Magnitude homology of geodesic metric spaces with an upper curvature bound, Algebr. Geom. Topol. 21 (2021) 647 MR4250513
2 Y Asao, K Izumihara, Geometric approach to graph magnitude homology, Homology Homotopy Appl. 23 (2021) 297 MR4170472
3 J A Barceló, A Carbery, On the magnitudes of compact sets in Euclidean spaces, Amer. J. Math. 140 (2018) 449 MR3783215
4 C Berger, T Leinster, The Euler characteristic of a category as the sum of a divergent series, Homology Homotopy Appl. 10 (2008) 41 MR2369022
5 R Bottinelli, T Kaiser, Magnitude homology, diagonality, and median spaces, Homology Homotopy Appl. 23 (2021) 121 MR4248724
6 S Cho, Quantales, persistence, and magnitude homology, preprint (2019) arXiv:1910.02905
7 J Chuang, A King, T Leinster, On the magnitude of a finite dimensional algebra, Theory Appl. Categ. 31 (2016) 63 MR3448619
8 H Gimperlein, M Goffeng, On the magnitude function of domains in Euclidean space, Amer. J. Math. 143 (2021) 939 MR4270261
9 P G Goerss, J F Jardine, Simplicial homotopy theory, 174, Birkhäuser (1999) MR1711612
10 K Gomi, Magnitude homology of geodesic space, preprint (2019) arXiv:1902.07044
11 K Gomi, Smoothness filtration of the magnitude complex, Forum Math. 32 (2020) 625 MR4095498
12 D Govc, R Hepworth, Persistent magnitude, J. Pure Appl. Algebra 225 (2021) MR4137712
13 Y Gu, Graph magnitude homology via algebraic Morse theory, preprint (2018) arXiv:1809.07240
14 R Hepworth, Magnitude cohomology, preprint (2018) arXiv:1807.06832
15 R Hepworth, S Willerton, Categorifying the magnitude of a graph, Homology Homotopy Appl. 19 (2017) 31 MR3683605
16 P S Hirschhorn, Model categories and their localizations, 99, Amer. Math. Soc. (2003) MR1944041
17 R A Horn, C R Johnson, Matrix analysis, Cambridge Univ. Press (2013) MR2978290
18 M Hovey, Model categories, 63, Amer. Math. Soc. (1999) MR1650134
19 B Jubin, On the magnitude homology of metric spaces, preprint (2018) arXiv:1803.05062
20 R Kaneta, M Yoshinaga, Magnitude homology of metric spaces and order complexes, Bull. Lond. Math. Soc. 53 (2021) 893 MR4275098
21 G M Kelly, Basic concepts of enriched category theory, 64, Cambridge Univ. Press (1982) 245 MR651714
22 F W Lawvere, Metric spaces, generalized logic, and closed categories, Rend. Sem. Mat. Fis. Milano 43 (1973) 135 MR352214
23 T Leinster, The Euler characteristic of a category, Doc. Math. 13 (2008) 21 MR2393085
24 T Leinster, The magnitude of metric spaces, Doc. Math. 18 (2013) 857 MR3084566
25 T Leinster, M W Meckes, The magnitude of a metric space: from category theory to geometric measure theory, from: "Measure theory in non-smooth spaces" (editor N Gigli), de Gruyter (2017) 156 MR3701739
26 S Mac Lane, Categories for the working mathematician, 5, Springer (1971) MR0354798
27 M W Meckes, Positive definite metric spaces, Positivity 17 (2013) 733 MR3090690
28 M W Meckes, Magnitude, diversity, capacities, and dimensions of metric spaces, Potential Anal. 42 (2015) 549 MR3306695
29 S P Novikov, Multivalued functions and functionals : an analogue of the Morse theory, Dokl. Akad. Nauk SSSR 260 (1981) 31 MR630459
30 orangeskid, Positive definite matrix over a non-Archimedean field, Mathematics Stack Exchange thread (2017)
31 O Ore, Theory of graphs, 38, Amer. Math. Soc. (1962) MR0150753
32 N Otter, Magnitude meets persistence: homology theories for filtered simplicial sets, preprint (2018) arXiv:1807.01540
33 A Papadopoulos, Metric spaces, convexity and nonpositive curvature, 6, Eur. Math. Soc. (2005) MR2132506
34 R Sazdanovic, V Summers, Torsion in the magnitude homology of graphs, preprint (2019) arXiv:1912.13483