Algebraic & Geometric Topology Volume 24, issue 1 (2024)

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Smith ideals of operadic algebras in monoidal model categories

David White and Donald Yau

Algebraic & Geometric Topology 24 (2024) 341–392

DOI: 10.2140/agt.2024.24.341

Bibliography

1	M G Barratt, P J Eccles, Γ⁺–structures, I : A free group functor for stable homotopy theory, Topology 13 (1974) 25 MR0348737
2	C Barwick, On left and right model categories and left and right Bousfield localizations, Homology Homotopy Appl. 12 (2010) 245 MR2771591
3	M Batanin, D White, Homotopy theory of algebras of substitudes and their localisation, Trans. Amer. Math. Soc. 375 (2022) 3569 MR4402670
4	M Batanin, D White, Left Bousfield localization without left properness, J. Pure Appl. Algebra 228 (2024) 107570 MR4670515
5	J M Boardman, R M Vogt, Homotopy invariant algebraic structures on topological spaces, 347, Springer (1973) MR0420609
6	B Chorny, D White, A variant of a Dwyer–Kan theorem for model categories, preprint (2018) arXiv:1805.05378
7	H Chu, R Haugseng, Enriched ∞–operads, Adv. Math. 361 (2020) 106913 MR4038556
8	B I Dundas, O Röndigs, P A Østvær, Enriched functors and stable homotopy theory, Doc. Math. 8 (2003) 409 MR2029170
9	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
10	Z Fiedorowicz, Constructions of E_n operads, preprint (1998) arXiv:math/9808089
11	B Fresse, Homotopy of operads and Grothendieck–Teichmüller groups, I : The algebraic theory and its topological background, 217, Amer. Math. Soc. (2017) MR3643404
12	E Getzler, J D S Jones, Operads, homotopy algebra and iterated integrals for double loop spaces, preprint (1994) arXiv:hep-th/9403055
13	R Haugseng, Algebras for enriched ∞–operads, preprint (2019) arXiv:1909.10042
14	M Hausmann, G–symmetric spectra, semistability and the multiplicative norm, J. Pure Appl. Algebra 221 (2017) 2582 MR3646319
15	P S Hirschhorn, Model categories and their localizations, 99, Amer. Math. Soc. (2003) MR1944041
16	M Hovey, Model categories, 63, Amer. Math. Soc. (1999) MR1650134
17	M Hovey, Spectra and symmetric spectra in general model categories, J. Pure Appl. Algebra 165 (2001) 63 MR1860878
18	M Hovey, Smith ideals of structured ring spectra, preprint (2014) arXiv:1401.2850
19	M Hovey, D White, An alternative approach to equivariant stable homotopy theory, Tbilisi Math. J. 2020 special issue (2020) 51
20	M W Johnson, D Yau, On homotopy invariance for algebras over colored PROPs, J. Homotopy Relat. Struct. 4 (2009) 275 MR2559644
21	N Johnson, D Yau, Bimonoidal categories, E_n–monoidal categories, and algebraic K–theory, III, preprint (2021)
22	J Lurie, Higher topos theory, 170, Princeton Univ. Press (2009) MR2522659
23	J Lurie, Higher algebra, book project (2017)
24	S Mac Lane, Categories for the working mathematician, 5, Springer (1998) MR1712872
25	M A Mandell, Equivariant symmetric spectra, from: "Homotopy theory : relations with algebraic geometry, group cohomology, and algebraic K–theory" (editors P Goerss, S Priddy), Contemp. Math. 346, Amer. Math. Soc. (2004) 399 MR2066508
26	M Markl, Models for operads, Comm. Algebra 24 (1996) 1471 MR1380606
27	J P May, The geometry of iterated loop spaces, 271, Springer (1972) MR0420610
28	G L Monaco, Vopěnka’s principle in ∞–categories, preprint (2021) arXiv:2105.04251
29	F Muro, Homotopy theory of nonsymmetric operads, Algebr. Geom. Topol. 11 (2011) 1541 MR2821434
30	D Pavlov, J Scholbach, Admissibility and rectification of colored symmetric operads, J. Topol. 11 (2018) 559 MR3830876
31	C Polcino Milies, S K Sehgal, An introduction to group rings, 1, Kluwer (2002) MR1896125
32	D G Quillen, Homotopical algebra, 43, Springer (1967) MR0223432
33	C Rezk, A model category for categories, preprint (2000)
34	S Schwede, Global homotopy theory, 34, Cambridge Univ. Press (2018) MR3838307
35	S Schwede, B E Shipley, Algebras and modules in monoidal model categories, Proc. Lond. Math. Soc. 80 (2000) 491 MR1734325
36	J D Stasheff, Homotopy associativity of H–spaces, I, Trans. Amer. Math. Soc. 108 (1963) 275 MR158400
37	J D Stasheff, Homotopy associativity of H–spaces, II, Trans. Amer. Math. Soc. 108 (1963) 293 MR0158400
38	D White, Model structures on commutative monoids in general model categories, J. Pure Appl. Algebra 221 (2017) 3124 MR3666740
39	D White, Substitudes, Bousfield localization, higher braided operads, and Baez–Dolan stabilization, Oberwolfach Rep. 46 (2021) 56
40	D White, Monoidal Bousfield localizations and algebras over operads, from: "Equivariant topology and derived algebra" (editors S Balchin, D Barnes, M Kędziorek, M Szymik), Lond. Math. Soc. Lect. Note Ser. 474, Cambridge Univ. Press (2022) 180 MR4327101
41	D White, M Batanin, Baez–Dolan stabilization via (semi-)model categories of operads, from: "Interactions between representation theory, algebraic topology and commutative algebra" (editors D Herbera, W Pitsch, S Zarzuela), Trends Math. 5, Birkhäuser (2015) 175
42	D White, D Yau, Bousfield localization and algebras over colored operads, Appl. Categ. Structures 26 (2018) 153 MR3749666
43	D White, D Yau, Comonadic coalgebras and Bousfield localization, preprint (2018) arXiv:1805.11536
44	D White, D Yau, Arrow categories of monoidal model categories, Math. Scand. 125 (2019) 185 MR4031046
45	D White, D Yau, Homotopical adjoint lifting theorem, Appl. Categ. Structures 27 (2019) 385 MR3975894
46	D White, D Yau, Right Bousfield localization and operadic algebras, Tbilisi Math. J. 2020 special issue (2020) 71
47	D White, D Yau, Right Bousfield localization and Eilenberg–Moore categories, High. Struct. 7 (2023) 22 MR4600456
48	D Yau, Colored operads, 170, Amer. Math. Soc. (2016) MR3444662
49	D Yau, M W Johnson, A foundation for PROPs, algebras, and modules, 203, Amer. Math. Soc. (2015) MR3329226