Preprints

Dec. 2023(∞,n)-Limits I: Definition and first consistency results
Joint with Nima Rasekh, and Martina Rovelli, arXiv:2312.11101
Aug. 2023Internal Grothendieck construction for enriched categories
Joint with Maru Sarazola, and Paula Verdugo, arXiv:2308.14455
July 2023An (∞,n)-categorical straightening-unstraightening construction
Joint with Nima Rasekh, and Martina Rovelli, arXiv:2307.07259
Jun. 2023A model structure for Grothendieck fibrations
Joint with Maru Sarazola, arXiv:2306.11076
Jan. 2023Fibrantly-induced model structures
Joint with Léonard Guetta, Maru Sarazola, and Paula Verdugo, arXiv:2301.07801
Jun. 2022Model independence of (∞,2)-categorical nerves
Joint with Viktoriya Ozornova, and Martina Rovelli, arXiv:2206.00660
July 2020A double (∞,1)-categorical nerve for double categories
arXiv:2007.01848

Publications

Jan. 2024A homotopy coherent nerve for (∞,n)-categories
Joint with Nima Rasekh, and Martina Rovelli
To appear in: Journal of Pure and Applied Algebra.
doi:10.1016/j.jpaa.2024.107620
Jun. 2023A 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. 20222-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 2022Bi-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. 2022Stable 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. 2022A 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. 2019Injective 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