Rune Haugseng

Notice: To the greatest extent I am legally able to, I refuse permission to use any of my work for AI training purposes.

Expository Articles

  1. Higher categories
    Invited contribution to the Encyclopedia of mathematical physics.

Research Publications

  1. Enriched ∞-categories via non-symmetric ∞-operads (with David Gepner)
    Advances in Mathematics 279 (2015) 575-716
    arXiv:1312.3178, doi:10.1016/j.aim.2015.02.007
  2. Rectification of enriched ∞-categories
    Algebraic and Geometric Topology 15-4 (2015) 1931-1982
    arXiv:1312.3881, doi:10.2140/agt.2015.15.1931
  3. Bimodules and natural transformations for enriched ∞-categories
    Homology, Homotopy and Applications 18 (2016) 71-98
    arXiv:1506.07341, doi:10.4310/HHA.2016.v18.n1.a5
  4. On a spectral sequence for the cohomology of infinite loop spaces (with Haynes Miller)
    Algebraic and Geometric Topology 16-5 (2016) 2911-2947
    arXiv:1302.1816, doi:10.2140/agt.2016.16.2911
  5. The higher Morita category of En-algebras
    Geometry and Topology 21-3 (2017) 1631-1730
    arXiv:1412.8459, doi:10.2140/gt.2017.21.1631
  6. Lax colimits and free fibrations in ∞-categories (with David Gepner and Thomas Nikolaus)
    Documenta Mathematica 22 (2017) 1225-1266
  7. On the equivalence between Θn-spaces and iterated Segal spaces
    Proceedings of the AMS 146(4) (2018) 1401-1415
    arXiv:1604.08480, doi:10.1090/proc/13695
  8. Iterated spans and classical topological field theories
    Mathematische Zeitschrift 289(3) (2018) 1427-1488
    arXiv:1409.0837, doi:10.1007/s00209-017-2005-x
  9. Two models for the homotopy theory of ∞-operads (with Hongyi Chu and Gijs Heuts)
    Journal of Topology 11(4) (2018) 856-872
    arXiv:1606.03826, doi:10.1112/topo.12071
  10. Linear Batalin-Vilkovisky quantization as a functor of ∞-categories (with Owen Gwilliam)
    Selecta Mathematica 24(2) (2018) 1247-1313
    arXiv:1608.01290, doi:10.1007/s00029-018-0396-0
  11. Enriched ∞-operads (with Hongyi Chu)
    Advances in Mathematics 361 (2020) 106913
    arXiv:1707.08049, doi:10.1016/j.aim.2019.106913
  12. Segal spaces, spans, and semicategories
    Proceedings of the AMS 149 (2021) 961-975
    arXiv:1901.08264, doi:10.1090/proc/15197
  13. Shifted coisotropic correspondences (with Valerio Melani and Pavel Safronov)
    Journal of the Institute of Mathematics of Jussieu 21(3) (2022) 785-849
    arXiv:1904.11312, doi:10.1017/S1474748020000274
  14. ∞-operads as analytic monads (with David Gepner and Joachim Kock)
    International Mathematics Research Notices 16 (2022) 12516-12624
    arXiv:1712.06469, doi:10.1093/imrn/rnaa332
  15. Homotopy-coherent algebra via Segal conditions (with Hongyi Chu)
    Advances in Mathematics 385 (2021) 107733
    arXiv:1907.03977, doi:10.1016/j.aim.2021.107733
  16. On (co)ends in ∞-categories
    Journal of Pure and Applied Algebra 226(2) (2021) 106819
    arXiv:2008.03758, doi:10.1016/j.jpaa.2021.106819
  17. On lax transformations, adjunctions, and monads in (∞,2)-categories
    Higher Structures 5(1) (2021) 244-281
  18. ∞-operads via symmetric sequences
    Mathematische Zeitschrift 301(1) (2022) 115-171
    arXiv:1708.09632, doi:10.1007/s00209-021-02881-w
  19. Free algebras through Day convolution (with Hongyi Chu)
    Algebraic and Geometric Topology 22(7) (2022) 3401-3458
    arXiv:2006.08269, doi:10.2140/agt.2022.22.3401
  20. ∞-operads as symmetric monoidal ∞-categories (with Joachim Kock)
    To appear in Publicacions Matemàtiques
  21. The AKSZ construction in derived algebraic geometry as an extended topological field theory (with Damien Calaque and Claudia Scheimbauer)
    To appear in Memoirs of the American Mathematical Society
  22. On distributivity in higher algebra I: The universal property of bispans (with Elden Elmanto)
    Compositio Mathematica 159(11) (2023) 2326–2415
    arXiv:2010.15722, doi:10.1112/s0010437x23007388
  23. Lax monoidal adjunctions, two-variable fibrations and the calculus of mates (with Fabian Hebestreit, Sil Linskens and Joost Nuiten)
    Proceedings of the London Mathematical Society 127(4) (2023) 889–957
    arXiv:2011.08808, doi:10.1112/plms.12548
  24. Two-variable fibrations, factorisation systems and ∞-categories of spans (with Fabian Hebestreit, Sil Linskens and Joost Nuiten)
    Forum of Mathematics Sigma 11 (2023) Paper no. e111
    arXiv:2011.11042, doi:10.1017/fms.2023.107

List of mistakes


  1. Algebras for enriched ∞-operads
  2. Envelopes for algebraic patterns (with Shaul Barkan and Jan Steinebrunner)
  3. From analytic monads to ∞-operads through Lawvere theories
  4. Enriched homotopy-coherent structures (with Hongyi Chu)
  5. Some remarks on higher Morita categories
  6. On the tensor product of enriched ∞-categories


Weakly enriched higher categories (30 April 2013)

Warning: This contains a number of non-trivial errors. In any case, essentially everything in here can now be found in a much nicer and (as far as I know) correct form among the papers above.