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
   Encyclopedia of mathematical physics. Vol. 4. Topology & geometry (2025) 1-23
   arXiv:2401.14311

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 E_n-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
   arXiv:1501.02161
7. On the equivalence between Θ_n-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
    arXiv:2002.01037
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)
    Publicacions Matemàtiques 68(1) (2024) 111-137
    arXiv:2106.12975, doi:10.5565/publmat6812406
21. The AKSZ construction in derived algebraic geometry as an extended topological field theory (with Damien Calaque and Claudia Scheimbauer)
    Memoirs of the American Mathematical Society 308 (2025) no. 1555
    arXiv:2108.02473, doi:10.1090/memo/1555
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
25. Algebras for enriched ∞-operads
    Algebraic and Geometric Topology 25(7) (2025) 3789–3811
    arXiv:1909.10042, doi:10.2140/agt.2025.25.3789
26. Envelopes for algebraic patterns (with Shaul Barkan and Jan Steinebrunner)
    Algebraic and Geometric Topology 25(9) (2025) 5319-5388
    arXiv:2208.07183, doi:10.2140/agt.2025.25.5319
27. Homotopical commutative rings and bispans (with Bastiaan Cnossen, Tobias Lenz and Sil Linskens)
    Journal of the London Mathematical Society 111(6) (2025) e70200
    arXiv:2403.06911, doi:10.1112/jlms.70200
28. Straightening for lax transformations and adjunctions of (∞,2)-categories (with Fernando Abellán and Andrea Gagna)
    Selecta Mathematica 31(4) (2025) 85
    arXiv:2404.03971, doi:10.1007/s00029-025-01084-z

List of mistakes

Preprints

1. From analytic monads to ∞-operads through Lawvere theories
   arXiv:2301.01199
2. Enriched homotopy-coherent structures (with Hongyi Chu)
   arXiv:2308.11502
3. Some remarks on higher Morita categories
   arXiv:2309.09761
4. On the tensor product of enriched ∞-categories
   arXiv:2311.13362
5. Normed equivariant ring spectra and higher Tambara functors (with Bastiaan Cnossen, Tobias Lenz and Sil Linskens)
   arXiv:2407.08399
6. Free fibrations, lax colimits and Kan extensions for (∞,2)-categories (with Fernando Abellán and Louis Martini)
   arXiv:2602.07604

Thesis

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.