Joachim Kock

Joachim Kock

Associate Professor

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    1. 2024
    2. Published

      ∞-operads as symmetric monoidal ∞-categories

      Haugseng, R. G. & Kock, Joachim, 2024, In: Publicacions Matematiques. 68, 1, p. 111 137 p.

      Research output: Contribution to journal › Journal article › Research › peer-review

    3. 2022

    4. Culf maps and edgewise subdivision

      Hackney, P. & Kock, Joachim, 20 Oct 2022.

      Research output: Working paper › Preprint › Research

    5. Free decomposition spaces

      Hackney, P. & Kock, Joachim, 20 Oct 2022, 32 p.

      Research output: Working paper › Preprint › Research

    6. Infinity-Operads as Analytic Monads

      Gepner, D., Haugseng, R. G. & Kock, Joachim, 2022, In: International Mathematics Research Notices. 2022, p. 12516-12624

      Research output: Contribution to journal › Journal article › Research › peer-review

    7. Tracelet Hopf Algebras and Decomposition Spaces (Extended Abstract)

      Behr, N. & Kock, Joachim, 2022, Proceedings of the Fourth International Conference on Applied Category Theory. Kishida, K. (ed.). arXiv preprint, p. 323-337 (Electronic Proceedings in Theoretical Computer Science, Vol. 372).

      Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings › Research

    8. Whole-grain Petri nets and processes

      Kock, Joachim, 2022, In: Journal of the ACM. 70, 1, p. 1-58

      Research output: Contribution to journal › Journal article › Research › peer-review

    9. 2021

    10. Every 2-Segal space is unital

      Feller, M., Garner, R., Kock, Joachim, Proulx, M. U. & Weber, M., Mar 2021, In: Communications in Contemporary Mathematics. 23, 2, 6 p., 2050055.

      Research output: Contribution to journal › Journal article › Research › peer-review

    11. Operadic categories and decalage

      Garner, R., Kock, Joachim & Weber, M., 22 Jan 2021, In: Advances in Mathematics. 377, 23 p., 107440.

      Research output: Contribution to journal › Journal article › Research › peer-review

    12. The incidence comodule bialgebra of the Baez-Dolan construction

      Kock, Joachim, 2021, In: Advances in Mathematics. 383, 79 p., 107693.

      Research output: Contribution to journal › Journal article › Research › peer-review

    13. 2020

    14. Decomposition Spaces and Restriction Species

      Galvez-Carrillo, I., Kock, Joachim & Tonks, A., Nov 2020, In: International Mathematics Research Notices. 2020, 21, p. 7558-7616 59 p.

      Research output: Contribution to journal › Journal article › Research › peer-review

    15. Decomposition spaces, incidence algebras and Mobius inversion II: Completeness, length filtration, and finiteness (vol 333, pg 1242, 2018)

      Galvez-Carrillo, I., Kock, Joachim & Tonks, A., 16 Sep 2020, In: Advances in Mathematics. 371, 6 p., 107267.

      Research output: Contribution to journal › Journal article › Research › peer-review

    16. DECOMPOSITION-SPACE SLICES ARE TOPOSES

      Kock, Joachim & Spivak, D., Jun 2020, In: Proceedings of the American Mathematical Society. 148, 6, p. 2317-2329 13 p.

      Research output: Contribution to journal › Journal article › Research › peer-review

    17. Antipodes of monoidal decomposition spaces

      Carlier, L. & Kock, Joachim, Mar 2020, In: Communications in Contemporary Mathematics. 22, 2, 15 p., 1850081.

      Research output: Contribution to journal › Journal article › Research › peer-review

    18. From Mobius inversion to renormalisation

      Kock, Joachim, 2020, In: Communications in Number Theory and Physics. 14, 1, p. 171-198 28 p.

      Research output: Contribution to journal › Journal article › Research › peer-review

    19. Operads of (noncrossing) partitions, interacting bialgebras, and moment-cumulant relations

      Kock, Joachim, Patras, F., Ebrahimi-Fard, K. & Foissy, L., 2020, In: Advances in Mathematics. 369, 107170.

      Research output: Contribution to journal › Journal article › Research › peer-review

    20. 2019

    21. Faa di Bruno for operads and internal algebras

      Kock, Joachim & Weber, M., Jun 2019, In: Journal of the London Mathematical Society. 99, 3, p. 919-944 26 p.

      Research output: Contribution to journal › Journal article › Research › peer-review

    22. 2018

    23. Decomposition spaces, incidence algebras and Mobius inversion III: The decomposition space of Mobius intervals

      Galvez-Carrillo, I., Kock, Joachim & Tonks, A., 20 Aug 2018, In: Advances in Mathematics. 334, p. 544-584 41 p.

      Research output: Contribution to journal › Journal article › Research › peer-review

    24. Decomposition spaces, incidence algebras and Möbius inversion II: Completeness, length filtration, and finiteness

      Gálvez-carrillo, I., Kock, Joachim & Tonks, A., 1 Jul 2018, In: Advances in Mathematics. 333, p. 1242-1292

      Research output: Contribution to journal › Journal article › Research › peer-review

    25. Homotopy linear algebra

      Galvez-Carrillo, I., Kock, Joachim & Tonks, A., Apr 2018, In: Proceedings of the Royal Society of Edinburgh Section A: Mathematics. 148, 2, p. 293-325 33 p.

      Research output: Contribution to journal › Journal article › Research › peer-review

    26. COSPAN CONSTRUCTION OF THE GRAPH CATEGORY OF BORISOV AND MANIN

      Kock, Joachim, 2018, In: Publicacions Matematiques. 62, 2, p. 331-353 23 p.

      Research output: Contribution to journal › Journal article › Research › peer-review

    27. Decomposition spaces, incidence algebras and Möbius inversion I: basic theory

      Gálvez Carrillo, M. I., Kock, Joachim & Tonks, A., 2018, In: Advances in Mathematics. 331, p. 952-1015

      Research output: Contribution to journal › Journal article › Research › peer-review

    28. REGULAR PATTERNS, SUBSTITUDES, FEYNMAN CATEGORIES AND OPERADS

      Batanin, M., Kock, Joachim & Weber, M., 2018, In: Theory and Applications of Categories. 33, p. 148-192 45 p.

      Research output: Contribution to journal › Journal article › Research › peer-review

    29. 2017

    30. Homotopy composition of cospans

      Kock, Joachim & Spivak, D. I., Oct 2017, In: Communications in Contemporary Mathematics. 19, 5, 6 p., 1650047.

      Research output: Contribution to journal › Journal article › Research › peer-review

    31. Univalence in locally cartesian closed infinity-categories

      Gepner, D. & Kock, Joachim, May 2017, In: Forum Mathematicum. 29, 3, p. 617-652 36 p.

      Research output: Contribution to journal › Journal article › Research › peer-review

    32. Hochster duality in derived categories and point-free reconstruction of schemes

      Kock, Joachim & Pitsch, W., 2017, In: Transactions of the American Mathematical Society. 369, 1, p. 223-261 39 p.

      Research output: Contribution to journal › Journal article › Research › peer-review

    33. Polynomial functors and combinatorial Dyson-Schwinger equations

      Kock, Joachim, 2017, In: Journal of Mathematical Physics. 58, 041703.

      Research output: Contribution to journal › Journal article › Research › peer-review

    34. 2016

    35. Combinatorial Dyson-Schwinger equations and inductive data types

      Kock, Joachim, Jun 2016, In: Frontiers of Physics. 11, 3, 15 p., 111205.

      Research output: Contribution to journal › Journal article › Research › peer-review

    36. Graphs, hypergraphs, and properads

      Kock, Joachim, May 2016, In: Collectanea Mathematica. 67, 2, p. 155-190 36 p.

      Research output: Contribution to journal › Journal article › Research › peer-review

    37. 2015

    38. Perturbative Renormalisation for Not-Quite-Connected Bialgebras

      Kock, Joachim, Oct 2015, In: Letters in Mathematical Physics. 105, 10, p. 1413-1425 13 p.

      Research output: Contribution to journal › Journal article › Research › peer-review

    39. 2014

    40. Groupoids and Faa di Bruno formulae for Green functions in bialgebras of trees

      Galvez-Carrillo, I., Kock, Joachim & Tonks, A., 20 Mar 2014, In: Advances in Mathematics. 254, p. 79-117 39 p.

      Research output: Contribution to journal › Journal article › Research › peer-review

    41. 2013

    42. Categorification of Hopf algebras of rooted trees

      Kock, Joachim, Mar 2013, In: Central European Journal of Mathematics. 11, 3, p. 401-422 22 p.

      Research output: Contribution to journal › Journal article › Research › peer-review

    43. Local fibred right adjoints are polynomial

      Kock, A. & Kock, Joachim, Feb 2013, In: Mathematical Structures in Computer Science. 23, 1, p. 131-141 11 p.

      Research output: Contribution to journal › Journal article › Research › peer-review

    44. Polynomial functors and polynomial monads

      Gambino, N. & Kock, Joachim, Jan 2013, In: Mathematical Proceedings of the Cambridge Philosophical Society. 154, 1, p. 153-192 40 p.

      Research output: Contribution to journal › Journal article › Research › peer-review

    45. COHERENCE FOR WEAK UNITS

      Joyal, A. & Kock, Joachim, 2013, In: Documenta Mathematica. 18, p. 71-110 40 p.

      Research output: Contribution to journal › Journal article › Research › peer-review

    46. 2012

    47. Data Types with Symmetries and Polynomial Functors over Groupoids

      Kock, Joachim, 24 Sep 2012, In: Electronic Notes in Theoretical Computer Science. 286, p. 351-365 15 p.

      Research output: Contribution to journal › Journal article › Research › peer-review

    48. Double adjunctions and free monads

      Kock, Joachim, Fiore, T. M. & Gambino, N., 2012, In: Cahiers de Topologie et Géométrie Différentielle Catégoriques. 53, p. 242-307

      Research output: Contribution to journal › Journal article › Research › peer-review

    49. 2011

    50. Monads in double categories

      Fiore, T. M., Gambino, N. & Kock, Joachim, Jun 2011, In: Journal of Pure and Applied Algebra. 215, 6, p. 1174-1197 24 p.

      Research output: Contribution to journal › Journal article › Research › peer-review

    51. Feynman graphs, and nerve theorem for compact symmetric multicategories (Extended Abstract)

      Joyal, A. & Kock, Joachim, 14 Feb 2011, In: Electronic Notes in Theoretical Computer Science. 270, 2, p. 105-113 9 p.

      Research output: Contribution to journal › Conference article › Research › peer-review

    52. Polynomial Functors and Trees

      Kock, Joachim, 2011, In: International Mathematics Research Notices. 2011, 3, p. 609-673 65 p.

      Research output: Contribution to journal › Journal article › Research › peer-review

    53. 2010

    54. Polynomial functors and opetopes

      Kock, Joachim, Joyal, A., Batanin, M. & Mascari, J., 20 Aug 2010, In: Advances in Mathematics. 224, 6, p. 2690-2737 48 p.

      Research output: Contribution to journal › Journal article › Research › peer-review

    55. 2008

    56. Elementary remarks on units in monoidal categories

      Kock, Joachim, Jan 2008, In: Mathematical Proceedings of the Cambridge Philosophical Society. 144, p. 53-76 24 p.

      Research output: Contribution to journal › Journal article › Research › peer-review

    57. 2007

    58. NOTE ON COMMUTATIVITY IN DOUBLE SEMIGROUPS AND TWO-FOLD MONOIDAL CATEGORIES

      Kock, Joachim, 2007, In: Journal of Homotopy and Related Structures. 2, 2, p. 217-228 12 p.

      Research output: Contribution to journal › Journal article › Research › peer-review

    59. Weak units and homotopy 3-types

      Joyal, A. & Kock, Joachim, 2007, CATEGORIES IN ALGEBRA, GEOMETRY AND MATHEMATICAL PHYSICS. Davydov, A., Batanin, M., Johnson, M., Lack, S. & Neeman, A. (eds.). AMER MATHEMATICAL SOC, p. 257-276 20 p. (Contemporary Mathematics, Vol. 431).

      Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings › Research › peer-review

    60. 2006

    61. An invitation to quantum cohomology: Kontsevich's formula for rational plane curves

      Kock, Joachim & Vainsencher, I., 2006, Birkhäuser Verlag. (Progress in Mathematics, Vol. 249).

      Research output: Book/Report › Book › Research › peer-review

    62. Weak identity arrows in higher categories

      Kock, Joachim, 2006, In: International Mathematics Research Papers. 54 p., 69163.

      Research output: Contribution to journal › Journal article › Research › peer-review

    63. 2005

    64. Simplicial localization of monoidal structures, and a non-linear version of Deligne's conjecture

      Kock, Joachim & Toen, B., Jan 2005, In: Compositio Mathematica. 141, 1, p. 253-261 9 p.

      Research output: Contribution to journal › Journal article › Research › peer-review

    65. 2004

    66. Tangency quantum cohomology

      Kock, Joachim, Jan 2004, In: Compositio Mathematica. 140, 1, p. 165-178 14 p.

      Research output: Contribution to journal › Journal article › Research › peer-review

    67. 2003

    68. Characteristic numbers of rational curves with cusp or prescribed triple contact

      Kock, Joachim, 2003, In: Mathematica Scandinavica. 92, 2, p. 223-245 23 p.

      Research output: Contribution to journal › Journal article › Research › peer-review

    69. Frobenius algebras and 2D topological quantum field theories

      Kock, Joachim, 2003, Cambridge University Press. (London Mathematical Society Student Texts, Vol. 59).

      Research output: Book/Report › Book › Research › peer-review

    70. 2002

    71. Descendant invariants and characteristic numbers

      Graber, T., Kock, Joachim & Pandharipande, R., Jun 2002, In: American Journal of Mathematics. 124, 3, p. 611-647 37 p.

      Research output: Contribution to journal › Journal article › Research › peer-review

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