3 papers
math.CT2026
Sphericalization and the Universal Spherical Adjunction
Fernando Abellán, Jonte Gödicke
For every adjunction of stable -categories -- or more generally, in any locally stable -category -- we give a simple procedure for inverting the twist and cotwi…
math.CT2026
Free fibrations, lax colimits and Kan extensions for -categories
Fernando Abellán, Rune Haugseng, Louis Martini
In the first part of this paper we study fibrations of -categories. We give a simple characterization of such fibrations in terms of a certain square being a pullback,…
math.CT2024
-Topoi and descent
Fernando Abellán, Louis Martini
We set the foundations of a theory of Grothendieck -topoi based on the notion of fibrational descent, which axiomatizes both the existence of a classifying object for f…