Preprints
| Aug. 2024 | (∞,n)-Limits II: Comparison across models Joint with Nima Rasekh, and Martina Rovelli, arXiv:2408.04742 |
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| Dec. 2023 | (∞,n)-Limits I: Definition and first consistency results Joint with Nima Rasekh, and Martina Rovelli, arXiv:2312.11101 |
| Aug. 2023 | Internal Grothendieck construction for enriched categories Joint with Maru Sarazola, and Paula Verdugo, arXiv:2308.14455 |
| July 2023 | An (∞,n)-categorical straightening-unstraightening construction Joint with Nima Rasekh, and Martina Rovelli, arXiv:2307.07259 |
| Jan. 2023 | Fibrantly-induced model structures Joint with Léonard Guetta, Maru Sarazola, and Paula Verdugo, arXiv:2301.07801 |
| Jun. 2022 | Model independence of (∞,2)-categorical nerves Joint with Viktoriya Ozornova, and Martina Rovelli, arXiv:2206.00660 |
Publications
| Nov. 2024 | Yoneda lemma and representation theorem for double categories Joint with Benedikt Fröhlich In: Theory and Applications of Categories. 41.49 (2024), pp. 1698-1782. tac:volume-41.49 |
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| Oct. 2024 | A model structure for Grothendieck fibrations Joint with Maru Sarazola In: Journal of Pure and Applied Algebra. 228.10 (2024), paper no. 107692, 29 pp. doi:10.1016/j.jpaa.2024.107692 |
| Jul. 2024 | A homotopy coherent nerve for (∞,n)-categories Joint with Nima Rasekh, and Martina Rovelli In: Journal of Pure and Applied Algebra. 228.7 (2024), paper no. 107620, 64 pp. doi:10.1016/j.jpaa.2024.107620 |
| Apr. 2024 | A double (∞,1)-categorical nerve for double categories To appear in: Annales de l’institut Fourier. arXiv:2007.01848 |
| Jun. 2023 | A model structure for weakly horizontally invariant double categories Joint with Maru Sarazola, and Paula Verdugo In: Algebraic and Geometric Topology. 23.4 (2023), pp. 1725-1786. doi:10.2140/agt.2023.23.1725 |
| Sep. 2022 | 2-limits and 2-terminal objects are too different Joint with tslil clingman In: Applied Categorical Structures. 30 (2022), pp. 1283–1304. doi:10.1007/s10485-022-09691-z |
| July 2022 | Bi-initial objects and bi-representations are not so different Joint with tslil clingman In: Cahiers de Topologie et Géométrie Différentielle Catégoriques. Volume LXIII-3 (2022), pp. 259-330. cahierstgdc:volume-lxiii-2022 |
| Jun. 2022 | Stable homotopy hypothesis in the Tamsamani model Joint with Viktoriya Ozornova, Simona Paoli, Maru Sarazola, and Paula Verdugo In: Topology and Its Applications. 2022. doi:10.1016/j.topol.2022.108106 |
| Apr. 2022 | A 2Cat-inspired model structure for double categories Joint with Maru Sarazola, and Paula Verdugo In: Cahiers de Topologie et Géométrie Différentielle Catégoriques. Volume LXIII-2 (2022), pp. 184-236. cahierstgdc:volume-lxiii-2022, extended version on arXiv:2004.14233 |
| Mar. 2019 | Injective and projective model structures on enriched diagram categories In: Homology, Homotopy, and Applications. 21.2 (2019), pp. 279-300. doi:10.4310/HHA.2019.v21.n2.a15 |
PhD and Master Thesis
PhD Thesis: Homotopical relations between 2-dimensional categories and their infinity-analogues
In my PhD thesis, I studied the homotopical relations between 2-dimensional categories and their ∞-analogues. It is a compilation of the papers A 2Cat-inspired model structure for double categories and A model structure for weakly horizontally invariant double categories, joint with Maru Sarazola and Paula Verdugo, and my paper A double (∞,1)-categorical nerve for double categories. In the first two papers, we construct two different model structures on the category of double categories which are compatible with Lack’s model structure on the category of 2-categories through the horizontal embedding. In the last paper, I construct a nerve functor from double categories to double (∞,1)-categories, which has the correct homotopical properties, and I show that it restricts along the horizontal embedding to a nerve functor from 2-categories to (∞,2)-categories in the form of 2-fold complete Segal spaces.
Master Thesis: Basic Localizers and Derivators