Publications of Joachim Kock

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Books

• Frobenius algebras and 2D topological quantum field theories
  No. 59 of LMSST, Cambridge University Press, 2003, xii+240pp.
• An invitation to quantum cohomology: Kontsevich’s formula for rational plane curves
  With Israel Vainsencher. No. 249 of Progress in Mathematics, Birkhäuser, 2006, xv+175pp.This is a revised English translation of
• A fórmula de Kontsevich para curvas racionais planas
  IMPA, Rio de Janeiro, 1999, xiv + 112pp.

Thesis

• Tangency quantum cohomology and enumerative geometry of rational curves
  PhD thesis, Universidade Federal de Pernambuco, Recife, Brazil, 2000, xx + 155pp.

Preprints

• Free loop spaces and the Cauchy-Frobenius Lemma
  With Thomas Jan Mikhail. ArXiv:2507.01637
• Convex decomposition spaces and Crapo complementation formula With Imma Gálvez and Andy Tonks. ArXiv:2409.03742
• Noncrossing arithmetics With Kurusch Ebrahimi-Fard, Loïc Foissy, and Frédéric Patras. ArXiv:2407.17660

Papers

• Abacus bicomodule configurations and the Bergner-Osorno-Ozornova-Rovelli-Scheimbauer equivalence
  With Thomas Jan Mikhail. To appear in Algebr. Geom. Topol. ArXiv:2501.16491
• Culf maps and edgewise subdivision
  With Philip Hackney. To appear in Trans. Amer. Math. Soc. ArXiv:2210.11191
• Decomposition spaces in combinatorics
  With Imma Gálvez and Andy Tonks. To appear in Higher Segal spaces and applications, Contemp. Math. AMS. ArXiv:1612.09225
• Free decomposition spaces
  With Philip Hackney. Collect. Math. 2024. https://doi.org/10.1007/s13348-024-00446-8. ArXiv:2210.11192
• ∞-operads as symmetric monoidal ∞-categories
  With Rune Haugseng. Publ. Mat. 68 (2024), 111–137.
• Whole-grain Petri nets and processes  J. ACM. 70 (2022), 1-58. (ArXiv:2005.05108)
• Tracelet Hopf algebras and decomposition spaces With Nicolas Behr. Proceedings of the 4th International Conference on Applied Category Theory ACT2021 (Cambridge, 2021), Electronic Proceedings in Theoretical Computer Science, 372 (2022), pp. 323-337. http://dx.doi.org/10.4204/EPTCS.372.23
• Infinity-Operads as Analytic Monads With David Gepner and Rune Haugseng. Int. Math. Res. Notices 2022, 12516-12624. LINK
• The incidence comodule bialgebra of the Baez-Dolan construction Adv. Math. 383 (2021), 107693. ArXiv:1912.11320
• Operadic categories and décalage With Richard Garner and Mark Weber. Adv. Math. 377 (2021), 107440. ArXiv:1812.01750
• Every 2-Segal space is unital With Matt Feller, Richard Garner, May Proulx, and Mark Weber. Commun. Contemp. Math. 23 (2021), 2050055. ArXiv:1905.09580
• Operads of (noncrossing) partitions, interacting bialgebras, and moment-cumulant relations With Kurusch Ebrahimi-Fard, Loïc Foissy, and Frédéric Patras.
  Adv. Math. 369 (2020), 107170. ArXiv:1907.01190
• Decomposition-space slices are toposes With David Spivak. Proc. Amer. Math. Soc. 148 (2020), 2317-2329. ArXiv:1807.06000
• From Möbius inversion to renormalisation Commun. Number Theory Phys. 14 (2020), 171-198. ArXiv:1809.00941
• Decomposition spaces and restriction species With Imma Gálvez and Andy Tonks. Int. Math. Res. Notices 2020 (2020), 7558-7616. LINK ArXiv:1708.02570
• Antipodes of monoidal decomposition spaces With Louis Carlier. Commun. Contemp. Math. 22 (2020), 1850081, 15pp. ArXiv:1807.11858
• Faà di Bruno for operads and internal algebras With Mark Weber. J. London Math. Soc. 99 (2019), 919-944. ArXiv:1609.03276
• Decomposition spaces, incidence algebras and Möbius inversion III: the decomposition space of Möbius intervals With Imma Gálvez and Andy Tonks. Adv. Math. 334 (2018), 544-584. ArXiv:1512.07580
• Decomposition spaces, incidence algebras and Möbius inversion II: completeness, length filtration, and finiteness With Imma Gálvez and Andy Tonks. Adv. Math. 333 (2018), 1242-1292. ArXiv:1512.07577
• Cospan construction of the graph category of Borisov and Manin Publ. Mat. 62 (2018), 331-353. (ArXiv:1611.10342)
• Decomposition spaces, incidence algebras and Möbius inversion I: basic theory With Imma Gálvez and Andy Tonks. Adv. Math. 331 (2018), 952-1015. ArXiv:1512.07573
• Regular patterns, substitudes, Feynman categories and operads With Michael Batanin and Mark Weber. Theory Appl. Categ. 33 (2018), 148-192.(ArXiv:1510.08934)
• Homotopy linear algebra With Imma Gálvez and Andy Tonks. Proc. Royal Soc. Edinburgh A 148 (2018), 293-325. (ArXiv:1602.05082)
• Polynomial functors and combinatorial Dyson-Schwinger equations J. Math. Phys. 58 (2017), 041703, 36pp. ArXiv:1512.03027
• Univalence in locally cartesian closed ∞-categories With David Gepner. Forum Math. 29 (2017), 617-652. ArXiv:1208.1749
• Homotopy composition of cospans With David Spivak. Commun. Contemp. Math. 19 (2017), 1650047, 6pp. ArXiv:1602.08739
• Hochster duality in derived categories and point-free reconstruction of schemes With Wolfgang Pitsch. Trans. Amer. Math. Soc. 369 (2017), 223-261. ArXiv:1305.1503
• Combinatorial Dyson-Schwinger equations and inductive data types Front. Phys. 11 (2016), 111205, pp.1-15. ArXiv:1512.07884
• Graphs, hypergraphs, and properads Collect. Math. 67 (2016), 155-190. ArXiv:1407.3744
• Perturbative renormalisation for not-quite-connected bialgebras Lett. Math. Phys. 105 (2015), 1413-1425. ArXiv:1411.3098
• Groupoids and Faà di Bruno formulae for Green functions in bialgebras of trees With Imma Gálvez and Andy Tonks. Adv. Math. 254 (2014), 79-117. ArXiv:1207.6404
• Coherence for weak units With André Joyal. Documenta Math. 18 (2013), 71-110. ArXiv:0907.4553
• Local fibered right adjoints are polynomial With Anders Kock. Math. Struct. Comput. Sci. 23 (2013), 131-141. ArXiv:1005.4236
• Categorification of Hopf algebras of rooted trees Cent. Eur. J. Math. 11 (2013), 401-422. ArXiv:1109.5785
• Polynomial functors and polynomial monads With Nicola Gambino. Math. Proc. Cambridge Phil. Soc. 154 (2013), 153-192. ArXiv:0906.4931
• Data types with symmetries and polynomial functors over groupoids Proceedings of the 28th Conference on the Mathematical Foundations of Programming Semantics, Bath 2012, Electronic Notes in Theoretical Computer Science 286 (2012), 351-365. ArXiv:1210.0828
• Double adjunctions and free monads With Tom Fiore and Nicola Gambino. Cahiers Topol. Géom. Différ. Catég. 53 (2012), 242-307. ArXiv:1105.6206
• Monads in double categories With Tom Fiore and Nicola Gambino. J. Pure Appl. Algebra 215 (2011), 1174-1197. ArXiv:1006.0797
• Feynman graphs, and nerve theorem for compact symmetric multicategories (extended abstract) With André Joyal. Proceedings of the 6th International Workshop on Quantum Physics and Logic (Oxford 2009), Electronic Notes in Theoretical Computer Science 270 (2011), 105-113. ArXiv:0908.2675
• Polynomial functors and trees Int. Math. Res. Notices 2011 (2011), 609-673. ArXiv:0807.2874
• Polynomial functors and opetopes With André Joyal, Michael Batanin, and Jean-François Mascari. Adv. Math. 224 (2010), 2690-2737. ArXiv:math/0706.1033
• Elementary remarks on units in monoidal categories Math. Proc. Cambridge Phil. Soc. 144 (2008), 53-76. ArXiv:math.CT/0507349
• Note on commutativity in double semigroups and two-fold monoidal categories Mac Lane Memorial Volume, J. Homotopy Rel. Struct. 2 (2007), 217-228. ArXiv:math.CT/0608452
• Weak units and homotopy 3-types With André Joyal. Street Festschrift: Categories in algebra, geometry and mathematical physics, Contemp. Math. 431 (2007), 257-276. ArXiv:math.CT/0602084
• Weak identity arrows in higher categories Int. Math. Res. Papers (2006), 1-54. ArXiv:math.CT/0507116
• Simplicial localisation of monoidal structures, and a non-linear version of Deligne’s conjecture With Bertrand Toën. Compositio Math. 141 (2005), 253-261. ArXiv:math.AT/0304442
• Tangency quantum cohomology Compositio Math. 140 (2004), 165-178. ArXiv:math.AG/0006148
• Characteristic numbers of rational curves with cusp or prescribed triple contact Math. Scand. 92 (2003), 223-245. ArXiv:math.AG/0102082
• Descendant invariants and characteristic numbers With Tom Graber and Rahul Pandharipande. Amer. J. Math. 124 (2002), 611-647.ArXiv:math.AG/0102017
• Tangency quantum cohomology and characteristic numbers An. Acad. Bras. Cienc. 73 (2001), 319-326.
• Frobenius splitting of complete intersections in Pⁿ Comm. Algebra 25 (1997), 1205-1213.