Algebraic & Geometric Topology Volume 20, issue 1 (2020)

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Incidence bicomodules, Möbius inversion and a Rota formula for infinity adjunctions

Louis Carlier

Algebraic & Geometric Topology 20 (2020) 169–213

DOI: 10.2140/agt.2020.20.169

Bibliography

1	M Aguiar, N Bergeron, F Sottile, Combinatorial Hopf algebras and generalized Dehn–Sommerville relations, Compos. Math. 142 (2006) 1 MR2196760
2	M Aguiar, W Ferrer Santos, Galois connections for incidence Hopf algebras of partially ordered sets, Adv. Math. 151 (2000) 71 MR1752242
3	M Aigner, Combinatorial theory, 234, Springer (1979) MR542445
4	D Ayala, J Francis, Fibrations of ∞–categories, preprint (2017) arXiv:1702.02681
5	J C Baez, J Dolan, From finite sets to Feynman diagrams, from: "Mathematics unlimited: 2001 and beyond" (editors B Engquist, W Schmid), Springer (2001) 29 MR1852152
6	J E Bergner, A M Osorno, V Ozornova, M Rovelli, C I Scheimbauer, 2–Segal sets and the Waldhausen construction, Topology Appl. 235 (2018) 445 MR3760213
7	L Carlier, Möbius functions of directed restriction species and free operads, via the generalised Rota formula, preprint (2018) arXiv:1812.09915
8	P Cartier, D Foata, Problèmes combinatoires de commutation et réarrangements, 85, Springer (1969) MR0239978
9	M Content, F Lemay, P Leroux, Catégories de Möbius et fonctorialités : un cadre général pour l’inversion de Möbius, J. Combin. Theory Ser. A 28 (1980) 169 MR563554
10	T Dyckerhoff, M Kapranov, Higher Segal spaces, I, 2244, Springer (2019)
11	I Gálvez-Carrillo, J Kock, A Tonks, Decomposition spaces in combinatorics, preprint (2016) arXiv:1612.09225
12	I Gálvez-Carrillo, J Kock, A Tonks, Decomposition spaces and restriction species, Int. Math. Res. Not. (2018)
13	I Gálvez-Carrillo, J Kock, A Tonks, Decomposition spaces, incidence algebras and Möbius inversion, I : Basic theory, Adv. Math. 331 (2018) 952 MR3804694
14	I Gálvez-Carrillo, J Kock, A Tonks, Decomposition spaces, incidence algebras and Möbius inversion, II : Completeness, length filtration, and finiteness, Adv. Math. 333 (2018) 1242 MR3818099
15	I Gálvez-Carrillo, J Kock, A Tonks, Homotopy linear algebra, Proc. Roy. Soc. Edinburgh Sect. A 148 (2018) 293 MR3777576
16	D Gepner, R Haugseng, J Kock, ∞–Operads as analytic monads, preprint (2017) arXiv:1712.06469
17	L Illusie, Complexe cotangent et déformations, II, 283, Springer (1972) MR0491681
18	A Joyal, Quasi-categories and Kan complexes, J. Pure Appl. Algebra 175 (2002) 207 MR1935979
19	A Joyal, The theory of quasi-categories and its applications, II, lecture notes (2008)
20	A Joyal, Distributors and barrels, preprint (2012)
21	P Leroux, Les catégories de Möbius, Cahiers Topologie Géom. Différentielle 16 (1975) 280
22	J Lurie, Higher topos theory, 170, Princeton Univ. Press (2009) MR2522659
23	J Lurie, Higher algebra, book project (2017)
24	M D Penney, Simplicial spaces, lax algebras and the 2–Segal condition, preprint (2017) arXiv:1710.02742
25	G C Rota, On the foundations of combinatorial theory, I : Theory of Möbius functions, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 2 (1964) 340 MR174487
26	R P Stanley, Enumerative combinatorics, I, Wadsworth & Brooks/Cole (1986) MR847717
27	T Walde, Hall monoidal categories and categorical modules, preprint (2016) arXiv:1611.08241
28	M B Young, Relative 2–Segal spaces, Algebr. Geom. Topol. 18 (2018) 975 MR3773745