Free bifibrations of (∞,2)-categories, 2-simplicial objects and the walking adjunction
ArXiv preprint
Fernando Abellán
Postdoctoral Researcher
Universität Regensburg
I work in higher category theory, with a focus on categorification and lax structures.
About Me
I am a postdoctoral researcher at the University of Regensburg, mentored by Denis-Charles Cisinski. My position is supported by the Collaborative Research Centre “Generalised Motivic Methods in Geometry” (CRC 1785), funded by the DFG.
Previously, I was a postdoctoral researcher at the Max Planck Institute for Mathematics in Bonn, mentored by Viktoriya Ozornova. Before that, I was a postdoctoral researcher at NTNU in Trondheim, working with Rune Haugseng.
I completed my PhD at the University of Hamburg, supervised by Tobias Dyckerhoff.
Higher category theoryHomotopy theoryCategorified homological algebraTopos theory
Education
- 2022
- PhD in Mathematics University of Hamburg
- 2019
- MSc in Mathematics University of Bonn
- 2016
- BSc in Mathematics & BSc in Physics Complutense University of Madrid
Publications and preprints
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Sphericalization and the Universal Spherical Adjunction
ArXiv preprint
(∞,2)-Topoi and descent
ArXiv preprint
View all 14 publicationsShow fewer publications
Straightening for lax transformations and adjunctions of (∞,2)-categories
Selecta Mathematica
Comparing lax functors of (∞,2)-categories
ArXiv preprint
On local fibrations of (∞,2)-categories
Algebraic & Geometric Topology vol 26, issue 5, 2026
On cofinal functors of ∞-bicategories
ArXiv preprint
2-Cartesian fibrations II: The Grothendieck construction for ∞-bicategories
Journal of the Institute of Mathematics of Jussieu
2-Cartesian fibrations I: A model for ∞-bicategories fibred in ∞-bicategories
Applied Categorical Structures, Volume 30, 2022
Enhanced twisted arrow categories
Theory and Applications of Categories, Volume 39, 2023
Marked colimits and higher cofinality
Journal of Homotopy and Related Structures, Volume 17, 2022
Theorem A for marked 2-categories
Journal of Pure and Applied Algebra, Volume 226, Issue 9, September 2022
A relative 2-nerve
Algebraic & Geometric Topology 20-6 (2020)
Selected talks and seminars
31 August–4 September, 2026
An (∞,2)-category of schobers on a surface
Stratifying Kiel · University of Kiel, Germany
15-16 August, 2024
(∞,2)-Topoi and descent
Norwegian Topology Meeting · NTNU (Trondheim)
4 June, 2024
Enhanced Segal objects and the Gray tensor product of (∞,2)-categories
Algebra & Topology seminar · University of Copenhagen
24 May, 2024
Enhanced Segal objects and the Gray tensor product of (∞, 2)-categories
Higher invariants seminar · University of Regensburg
15-19 April, 2024
Enhanced Segal objects and the Gray tensor product of (∞,2)-categories
(∞,n)-Categories and their applications · Utrecht University
3-7 July, 2023
Local fibrations of (∞,2)-categories and the Grothendieck construction
29th Nordic Congress of Mathematicians · Aalborg University
5 February, 2021
Marked colimits and higher cofinality
CRM Intensive Research Program on Higher Homotopical Structures · Centre de Recerca Matemàtica, Barcelona
Contact
abellan@mpim-bonn.mpg.deUniversität Regensburg
93040 Regensburg, Germany