7 papers
Day convolution for algebraic patterns
Thomas Blom, Félix Loubaton, Jaco Ruit
We characterize the exponentiable objects for a wide range of structures prevalent in -categorical algebra, extending the construction of Day convolution to more general st…
On the squares functor and the Gaitsgory-Rozenblyum conjectures
Félix Loubaton, Jaco Ruit
In the seminal work of Gaitsgory and Rozenblyum on derived algebraic geometry, eight conjectures regarding the theory of -categories are stated. This paper aims to clar…
Effectivity of Generalized Double -Categories
Félix Loubaton
We construct an adjunction between -categories internal to -categories, called -double -categories, and filtrations where for al…
A model for the coherent walking -equivalence
Amar Hadzihasanovic, Félix Loubaton, Viktoriya Ozornova +1
We prove that a certain -category, which was constructed in previous work by the third and fourth author, is a model for the fully coherent walking -equivalence. Further, app…
Theory and models of -categories
Félix Loubaton
This thesis is divided into two parts. In the first part, we study models of -categories. The main result is to establish a Quillen equivalence between Rezk's complete…
The complicial model of -categories
Félix Loubaton
In this text, we show that Verity -complicial sets are a model of (non-complete) -categories.
Dualities in the complicial model of -categories
Félix Loubaton
In this note, we study the connection between Gray tensor product and suspension. We derive a characterization of weak equivalences as fully faithful and essentially surjective fun…