1 citations · 4 across the 9 of their papers we have counts for
9 papers
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,…
The condensed homotopy type of a scheme
Peter J. Haine, Tim Holzschuh, Marcin Lara +3
We study a condensed version of the étale homotopy type of a scheme, which refines both the usual étale homotopy type of Friedlander-Artin-Mazur and the proétale fundamental group…
-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…
Proper morphisms of -topoi
Louis Martini, Sebastian Wolf
We characterise proper morphisms of -topoi in terms of a relativised notion of compactness: we show that a geometric morphism of -topoi is proper if and only if it…
Internal higher topos theory
Louis Martini, Sebastian Wolf
We develop the theory of topoi internal to an arbitrary -topos . We provide several characterisations of these, including an internal analogue of Lurie's charac…
Presentability and topoi in internal higher category theory
Louis Martini, Sebastian Wolf
The goal of this article is to develop the theory of presentable categories and topoi internal to an arbitrary -topos . Our main results are internal analogues…
Cocartesian fibrations and straightening internal to an -topos
Louis Martini
We define and study cartesian and cocartesian fibrations between categories internal to an -topos and prove a straightening equivalence in this context.
Colimits and cocompletions in internal higher category theory
Louis Martini, Sebastian Wolf
We develop a number of basic concepts in the theory of categories internal to an -topos. We discuss adjunctions, limits and colimits as well as Kan extensions for internal…
Yoneda's lemma for internal higher categories
Louis Martini
We develop some basic concepts in the theory of higher categories internal to an arbitrary -topos. We define internal left and right fibrations and prove a version of the G…