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

• Free decomposition spaces
  With Philip Hackney. ArXiv:2210.11192
• Culf maps and edgewise subdivision
  With Philip Hackney. ArXiv:2210.11191
• ∞-operads as symmetric monoidal ∞-categories
  With Rune Haugseng. To appear in Publ. Mat. ArXiv:2106.12975
• Decomposition spaces in combinatorics
  With Imma Gálvez and Andy Tonks. ArXiv:1612.09225

Papers

• Whole-grain Petri nets and processes
  J. ACM. 70 (2022), 1-58. https://doi.org/10.1145/3559103
  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 ArXiv:2105.06186.
• Infinity-Operads as Analytic Monads
  With David Gepner and Rune Haugseng. Int. Math. Res. Notices 2022, 12516-12624. LINK ArXiv:1712.06469
• 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.
  

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)