Publications of Joachim Kock

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

• J. Kock and J. M. Møller. Signs in objective linear algebra, exemplified with exterior powers and determinants. [ArXiv:2603.19437]
• J. Kock and J. M. Møller. Groupoid G-spans and matrices over group rings. [ArXiv:2603.20787]
• M. Batanin, J. Kock, and M. Weber. Pita factorisation in operadic categories. [ArXiv:2512.22794]
• J. Kock and T. J. Mikhail. Free loop spaces and the Cauchy-Frobenius Lemma. [ArXiv:2507.01637]
• I. Gálvez, J. Kock, and A. Tonks. Convex decomposition spaces and Crapo complementation formula. [ArXiv:2409.03742]
• K. Ebrahimi-Fard, L. Foissy, J. Kock. and F. Patras. Noncrossing arithmetic. To appear in Category Theory at Work in Computational Mathematics and Theoretical Informatics (Bergen 2023), Fund. Struct. Comput. Pure Math., Birkhäuser (2026). [ArXiv:2407.17660]

Papers

• J. Kock and T. J. Mikhail. Abacus bicomodule configurations and the Bergner-Osorno-Ozornova-Rovelli-Scheimbauer equivalence. To appear in Algebr. Geom. Topol. [ArXiv:2501.16491]
• I. Gálvez, J. Kock, and A. Tonks. Decomposition spaces in combinatorics. In: Higher Segal spaces and applications (Banff 2024), Vol.838 of Contemp. Math., AMS (2026) [ArXiv:1612.09225]
• P. Hackney and J. Kock. Culf maps and edgewise subdivision. With an appendix coauthored with J. Steinebrunner. Trans. Amer. Math. Soc. 379 (2026), 2955-3007. [ArXiv:2210.11191]
• P. Hackney and J. Kock. Free decomposition spaces. Collect. Math. 76 (2025), 575-599. [ArXiv:2210.11192]
• R. Haugseng and J. Kock. ∞-operads as symmetric monoidal ∞-categories. Publ. Mat. 68 (2024), 111-137.
• J. Kock. Whole-grain Petri nets and processes. J. ACM. 70 (2022), 1-58.
• N. Behr and J. Kock. Tracelet Hopf algebras and decomposition spaces. 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. [ArXiv:2105.06186]
• D. Gepner, R. Haugseng, and J. Kock. Infinity-Operads as Analytic Monads. Int. Math. Res. Notices 2022, 12516-12624. LINK [ArXiv:1712.06469]
• J. Kock. The incidence comodule bialgebra of the Baez-Dolan construction. Adv. Math. 383 (2021), 107693. [ArXiv:1912.11320]
• R. Garner, J. Kock, and M. Weber.Operadic categories and décalage. Adv. Math. 377 (2021), 107440. [ArXiv:1812.01750]
• M. Feller, R. Garner, J. Kock, M. Proulx, and M. Weber. Every 2-Segal space is unital. Commun. Contemp. Math. 23 (2021), 2050055. [ArXiv:1905.09580]
• K. Ebrahimi-Fard, L. Foissy, J. Kock. and F. Patras. Operads of (noncrossing) partitions, interacting bialgebras, and moment-cumulant relations. Adv. Math. 369 (2020), 107170. [ArXiv:1907.01190]
• J. Kock and D. Spivak. Decomposition-space slices are toposes. Proc. Amer. Math. Soc. 148 (2020), 2317-2329. [ArXiv:1807.06000]
• J. Kock. From Möbius inversion to renormalisation. Commun. Number Theory Phys. 14 (2020), 171-198. [ArXiv:1809.00941]
• I. Gálvez, J. Kock, and A. Tonks. Decomposition spaces and restriction species. Int. Math. Res. Notices 2020 (2020), 7558-7616. LINK [ArXiv:1708.02570]
• L. Carlier and J. Kock. Antipodes of monoidal decomposition spaces. Commun. Contemp. Math. 22 (2020), 1850081, 15pp. [ArXiv:1807.11858]
• J. Kock and M. Weber. Faà di Bruno for operads and internal algebras. J. London Math. Soc. 99 (2019), 919-944. [ArXiv:1609.03276]
• I. Gálvez, J. Kock, and A. Tonks. Decomposition spaces, incidence algebras and Möbius inversion III: the decomposition space of Möbius intervals. Adv. Math. 334 (2018), 544-584. [ArXiv:1512.07580]
• I. Gálvez, J. Kock, and A. Tonks. Decomposition spaces, incidence algebras and Möbius inversion II: completeness, length filtration, and finiteness. Adv. Math. 333 (2018), 1242-1292. [ArXiv:1512.07577]
• J. Kock. Cospan construction of the graph category of Borisov and Manin. Publ. Mat. 62 (2018), 331-353. [ArXiv:1611.10342]
• I. Gálvez, J. Kock, and A. Tonks. Decomposition spaces, incidence algebras and Möbius inversion I: basic theory . Adv. Math. 331 (2018), 952-1015. [ArXiv:1512.07573]
• M. Batanin, J. Kock, and M. Weber. Regular patterns, substitudes, Feynman categories and operads. Theory Appl. Categ. 33 (2018), 148-192. [ArXiv:1510.08934]
• I. Gálvez, J. Kock, and A. Tonks. Homotopy linear algebra. 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]
• I. Gálvez, J. Kock, and A. Tonks. Groupoids and Faà di Bruno formulae for Green functions in bialgebras of trees. 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.

Misc

• Incidence Hopf algebras
  (Notes 2010. 11 pages.)
• Polynomial functors
  Rough draft (2009), 420pp.
• Spectra, supports, and Hochster duality
  (HOCAT talk and letter to Giordano Favi and Paul Balmer, December 2007. 12 pages.)
• Notes on Tamsamani categories, Segal categories, and applications.
  (Notes from two talks of Bertrand Toën in Minneapolis, 2004.)
• Notes on psi-classes
  (Notes 2001. 71 pages.)
• Géométrie énumérative et théorie d'intersection
  Notes (in French), 10pp.
• Geometria enumerativa de curvas racionais
  Notes (in Portuguese), 10pp.
• Classes características
  (24pp., abril 1997)
• O teorema de Grothendieck-Riemann-Roch
  (11pp., agosto 1997)