Martina Rovelli's webpage

These papers develop certain aspects of the theory of ω-categories.

• A model for the coherent walking ω-equivalence, with A.Hadzihasanovic, F.Loubaton, V.Ozornova, 2024: Proc. Amer. Math. Soc.: arXiv

• What is an equivalence in a higher category?, with V.Ozornova, 2023, Bull. London Math.: arXiv, doi

• A categorical characterization of strong Steiner ω-categories, with D.Ara, A.Gagna and V.Ozornova, 2022, J. Pure Appl. Algebra: arXiv, doi

• Nerves and cones of free loop-free ω-categories, with A.Gagna and V.Ozornova, 2021, Tunis. J. Math.: arXiv, pdf

These papers develop certain aspects of the theory of (∞,n)-categories or new model categories for (∞,n)-categories for general n.

• (∞,n)-Limits II: Comparison across models, with L.Moser and N.Rasekh, 2024: arXiv

• (∞,n)-Limits I: Definition and first consistency results, with L.Moser and N.Rasekh, 2023: arXiv

• An (∞,n)-categorical straightening-unstraightening construction, with L.Moser and N.Rasekh, 2023: arXiv

• A homotopy coherent nerve for (∞,n)-categories, with L.Moser and N.Rasekh, 2022, J. Pure Appl. Algebra: arXiv, doi, pdf

• A Quillen adjunction between globular and complicial approaches to (∞,n)-categories, with V.Ozornova, 2022, Adv. Math: arXiv, doi

• Gray tensor product and saturated N-complicial sets, with V.Ozornova and D.Verity, 2020: High. Struct.: arXiv, doi, pdf

• Fundamental pushouts of n-complicial sets, with V.Ozornova, 2020, High. Struct.: arXiv, doi, pdf

• Model structures for (∞,n)-categories on (pre)stratified simplicial sets and spaces, with V.Ozornova, 2018, Algebr. Geom. Topol.: arXiv, doi

These papers develop certain aspects of the theory of (∞,2)-categories or new model categories for (∞,2)-categories. Most of my work focuses on the model of 2-complicial sets.

• Model independence of (∞,2)-categorical nerves, with L.Moser and V.Ozornova, 2022: arXiv

• An (∞,2)-categorical pasting theorem, with P.Hackney, V.Ozornova and E.Riehl, 2021, Trans. Am. Math. Soc.: arXiv, doi

• An explicit comparison between Θ_2-spaces and 2-complicial sets, with J.Bergner and V.Ozornova, 2021: Algebr. Geom. Topol.: arXiv

• The Duskin nerve of 2-categories in Joyal's cell category Θ_2, with V.Ozornova, 2019, J. Pure Appl. Algebra: arXiv, doi

• Nerves of 2-categories and categorification of (∞,2)-categories, with V.Ozornova, 2019, Adv. Math: arXiv, doi

These papers develop certain aspects of the theory of (∞,1)-categories or new model categories for (∞,1)-categories.

• Pushouts of Dwyer maps are (∞,1)-categorical, with P.Hackney, V.Ozornova and E.Riehl, 2022 Algebr. Geom. Topol.: arXiv, doi

• Induced model structures for ∞-categories and ∞-groupoids, with P.Hackney, 2021, Proc. Amer. Math. Soc.: arXiv, doi

• Weighted limits in an (∞,1)-category, 2019, Appl. Categorical Struct.: arXiv, doi, pdf

• A model structure on prederivators for (∞,1)-categories, with D.Fuentes-Keuthan and M.Kedziorek, 2018, Theory Appl. Categ.: arXiv, doi, pdf

This series of papers is on the topic of 2-Segal spaces and their relation with the Waldhausen construction.

• Comparison of Waldhausen constructions, with J.Bergner, A.Osorno, V.Ozornova and C.Scheimbauer, 2019, Ann. K-Theory: arXiv, doi

• 2-Segal objects and the Waldhausen construction, with J.Bergner, A.Osorno, V.Ozornova and C.Scheimbauer, 2018, Algebr. Geom. Topol.: arXiv, doi

• The edgewise subdivision criterion for 2-Segal objects, with J.Bergner, A.Osorno, V.Ozornova and C.Scheimbauer, 2018, Proc. Amer. Math. Soc.: arXiv, doi

• The unit of the total décalage adjunction, with V.Ozornova, 2017, J. Homotopy Relat. Struct. arXiv, doi

• 2-Segal sets and the Waldhausen construction, with J.Bergner, A.Osorno, V.Ozornova and C.Scheimbauer, 2016, Topology Appl.: arXiv, doi

My PhD thesis focuses on the study of homotopy invariants of principal bundles and geometric interpretations of characteristic classes.

• Towards new invariants for principal bundles, 2017: PhD Thesis, EPFL doi

• Characteristic classes as complete obstructions, 2016, J. Homotopy Relat. Struct. arXiv, doi pdf

• A looping-delooping adjunction for topological spaces, 2015, Homology Homotopy Appl.: arXiv, doi, pdf