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The right angled Artin group functor as a categorical embedding

Chris Grossack

Algebraic & Geometric Topology 25 (2025) 3035–3048
Bibliography
1 J Adámek, H Herrlich, G E Strecker, Abstract and concrete categories: the joy of cats, Wiley (1990) MR1051419
2 J Adámek, J Rosický, E M Vitale, Algebraic theories: a categorical introduction to general algebra, 184, Cambridge Univ. Press (2011) MR2757312
3 I Agol, The virtual Haken conjecture, Doc. Math. 18 (2013) 1045 MR3104553
4 V Arvind, P J Cameron, Recognizing the commuting graph of a finite group, preprint (2022) arXiv:2206.01059
5 S Awodey, J Hughes, The coalgebraic dual of Birkhoff’s variety theorem, technical report (2000)
6 B Baumeister, A Stein, Commuting graphs of odd prime order elements in simple groups, preprint (2009) arXiv:0908.2583
7 J Beck, Monadicity theorem, unpublished notes (1968)
8 M Bestvina, Geometric group theory and 3-manifolds hand in hand : the fulfillment of Thurston’s vision, Bull. Amer. Math. Soc. 51 (2014) 53 MR3119822
9 M Bojańczyk, Recognisable languages over monads, from: "Developments in language theory" (editor I Potapov), Lecture Notes in Comput. Sci. 9168, Springer (2015) 1 MR3440657
10 F Borceux, Handbook of categorical algebra, II: Categories and structures, 51, Cambridge Univ. Press (1994) MR1313497
11 F Borceux, S Caenepeel, G Janelidze, Monadic approach to Galois descent and cohomology, Theory Appl. Categ. 23 (2010) 92 MR2593387
12 P J Cameron, Graphs defined on groups, Int. J. Group Theory 11 (2022) 53 MR4346241
13 M Casals-Ruiz, A Duncan, I Kazachkov, Embedddings between partially commutative groups: two counterexamples, J. Algebra 390 (2013) 87 MR3072113
14 R Charney, An introduction to right-angled Artin groups, Geom. Dedicata 125 (2007) 141 MR2322545
15 J Culbertson, K Sturtz, A categorical foundation for Bayesian probability, Appl. Categ. Structures 22 (2014) 647 MR3227610
16 G Dolinar, B Kuzma, P Oblak, On maximal distances in a commuting graph, Electron. J. Linear Algebra 23 (2012) 243 MR2889585
17 C Droms, Isomorphisms of graph groups, Proc. Amer. Math. Soc. 100 (1987) 407 MR891135
18 R Flores, D Kahrobaei, T Koberda, Expanders and right-angled Artin groups, J. Topol. Anal. 16 (2024) 155 MR4751404
19 N Ghani, C Lüth, F d Marchi, J Power, Algebras, coalgebras, monads and comonads, Electron. Notes Theor. Comput. Sci. 44 (2001) 128
20 M Giry, A categorical approach to probability theory, from: "Categorical aspects of topology and analysis" (editor B Banaschewski), Lecture Notes in Math. 915, Springer (1982) 68 MR659884
21 M Giudici, A Pope, The diameters of commuting graphs of linear groups and matrix rings over the integers modulo m, Australas. J. Combin. 48 (2010) 221 MR2732115
22 E Green, Graph products of groups, PhD thesis, University of Leeds (1990)
23 A Grothendieck, Technique de descente et théorèmes d’existence en géométrie algébrique, I : Généralités. Descente par morphismes fidèlement plats, from: "Séminaire Bourbaki, 1958–1960", Benjamin (1959) MR1603475
24 M Hyland, J Power, The category theoretic understanding of universal algebra : Lawvere theories and monads, from: "Computation, meaning, and logic : articles dedicated to Gordon Plotkin" (editors L Cardelli, M Fiore, G Winskel), Electron. Notes Theor. Comput. Sci. 172, Elsevier (2007) 437 MR2328298
25 S h Kim, T Koberda, Embedability between right-angled Artin groups, Geom. Topol. 17 (2013) 493 MR3039768
26 S H Kim, T Koberda, The geometry of the curve graph of a right-angled Artin group, Internat. J. Algebra Comput. 24 (2014) 121 MR3192368
27 T Koberda, Right-angled Artin groups and a generalized isomorphism problem for finitely generated subgroups of mapping class groups, Geom. Funct. Anal. 22 (2012) 1541 MR3000498
28 T Koberda, Geometry and combinatorics via right-angled Artin groups, from: "In the tradition of Thurston, II : Geometry and groups" (editors K Ohshika, A Papadopoulos), Springer (2022) 475 MR4472060
29 T Leinster, Codensity and the ultrafilter monad, Theory Appl. Categ. 28 (2013) 332 MR3080612
30 J Meier, L Van Wyk, The Bieri–Neumann–Strebel invariants for graph groups, Proc. London Math. Soc. 71 (1995) 263 MR1337468
31 C F Miller III, Decision problems for groups—survey and reflections, from: "Algorithms and classification in combinatorial group theory" (editors G Baumslag, I Miller C. F.), Math. Sci. Res. Inst. Publ. 23, Springer (1992) 1 MR1230627
32 C F Miller III, P E Schupp, Some presentations of the trivial group, from: "Groups, languages and geometry" (editor R H Gilman), Contemp. Math. 250, Amer. Math. Soc. (1999) 113 MR1732210
33 E Moggi, Notions of computation and monads, Inform. and Comput. 93 (1991) 55 MR1115262
34 B H Neumann, A problem of Paul Erdős on groups, J. Austral. Math. Soc. Ser. A 21 (1976) 467 MR419283
35 V de Paiva, Dialectica comonads, from: "9th Conference on Algebra and Coalgebra in Computer Science" (editors F Gadducci, A Silva), Leibniz Int. Proc. Inform. 211, Schloss Dagstuhl (2021) 3 MR4390198
36 J J M M Rutten, Universal coalgebra: a theory of systems, Theoret. Comput. Sci. 249 (2000) 3 MR1791953
37 L Sabalka, On rigidity and the isomorphism problem for tree braid groups, Groups Geom. Dyn. 3 (2009) 469 MR2516176
38 H Servatius, Automorphisms of graph groups, J. Algebra 126 (1989) 34 MR1023285
39 H Servatius, C Droms, B Servatius, Surface subgroups of graph groups, Proc. Amer. Math. Soc. 106 (1989) 573 MR952322