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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…
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,…
-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…
Straightening for lax transformations and adjunctions of -categories
Fernando Abellán, Andrea Gagna, Rune Haugseng
We prove an unstraightening result for lax transformations between functors from an arbitrary -category to that of -categories. We apply this to study parti…
Comparing lax functors of -categories
Fernando Abellán
In this work, we study oplax normalised functors of -categories. Our main theorem is a comparison between the notion of oplax normalised functor of scaled simplicial se…