nLab Ulrik Buchholtz

• webpage

Selected writings

On varieties of cubical sets:

• Ulrik Buchholtz, Edward Morehouse, (2017). Varieties of Cubical Sets. In: Peter Höfner, Damien Pous, Georg Struth (eds) Relational and Algebraic Methods in Computer Science. RAMICS 2017. Lecture Notes in Computer Science, vol 10226. Springer, Cham. (doi:10.1007/978-3-319-57418-9_5, arXiv:1701.08189)

On cellular cohomology formulated in homotopy type theory:

• Ulrik Buchholtz, Kuen-Bang Hou (Favonia), Cellular Cohomology in Homotopy Type Theory, Logical Methods in Computer Science, Volume 16, Issue 2 (June 1, 2020) (arXiv:1802.02191, lmcs:6518)

Discussion of ∞-groups from the point of view of homotopy type theory:

• Ulrik Buchholtz, Floris van Doorn, Egbert Rijke, Higher Groups in Homotopy Type Theory, LICS ‘18: Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science (2018) 205-214 [arXiv:1802.04315, doi:10.1145/3209108.3209150]

• Ulrik Buchholtz, Notes on higher groups and projective spaces, 2016 (pdf)

On symmetry and introducing the language of homotopy type theory for univalent foundations of mathematics:

• Marc Bezem, Ulrik Buchholtz, Pierre Cagne, Bjørn Ian Dundas, Daniel R. Grayson: Symmetry (2021) $[$pdf$]$

On $(\infty,1)$-category theory:

• Ulrik Buchholtz, Jonathan Weinberger, Synthetic fibered $(\infty,1)$-category theory $[$arXiv:2105.01724, talk slides$]$

• Daniel Gratzer, Jonathan Weinberger, Ulrik Buchholtz, Directed univalence in simplicial homotopy type theory (arXiv:2407.09146)

• Daniel Gratzer, Jonathan Weinberger, Ulrik Buchholtz, The Yoneda embedding in simplicial type theory (arXiv:2501.13229)

On delooping, H-spaces and Eilenberg-MacLane spaces in homotopy type theory:

• Ulrik Buchholtz, J. Daniel Christensen, Jarl G. Taxerås Flaten, Egbert Rijke, Central H-spaces and banded types [arXiv:2301.02636]

On higher structures in homotopy type theory:

• Ulrik Buchholtz, Higher Structures in Homotopy Type Theory, in: Reflections on the Foundations of Mathematics, Synthese Library 407 Springer (2019) [doi:10.1007/978-3-030-15655-8_7, arXiv:1807.02177]

On epimorphisms and acyclic types in univalent type theory:

• Ulrik Buchholtz, Tom de Jong, Egbert Rijke, Epimorphisms and Acyclic Types in Univalent Mathematics, (arXiv:2401.14106)

On a dependent type theory conservative extension of primitive recursive arithmetic:

• Ulrik Buchholtz, Johannes Schipp von Branitz, Primitive Recursive Dependent Type Theory (arXiv:2404.01011)

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