8 citations · 18 across the 8 of their papers we have counts for
10 papers
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…
A categorical characterization of strong Steiner -categories
Dimitri Ara, Andrea Gagna, Viktoriya Ozornova +1
Strong Steiner -categories are a class of -categories that admit algebraic models in the form of chain complexes, whose formalism allows for several explicit computations. Th…
Cartesian Fibrations of -categories
Andrea Gagna, Yonatan Harpaz, Edoardo Lanari
In this article we introduce four variance flavours of cartesian 2-fibrations of -bicategories with -bicategorical fibres, in the framework of scaled simplicial set…
Bilimits are Bifinal Objects
Andrea Gagna, Yonatan Harpaz, Edoardo Lanari
We prove that a (lax) bilimit of a 2-functor is characterized by the existence of a limiting contraction in the 2-category of (lax) cones over the diagram. We also investigate the…
Nerves and cones of free loop-free ω-categories
Andrea Gagna, Viktoriya Ozornova, Martina Rovelli
We show that the complicial nerve construction is homotopically compatible with two flavors of cone constructions when starting with an -category that is suitably free and loop-…
Fibrations and lax limits of -categories
Andrea Gagna, Yonatan Harpaz, Edoardo Lanari
We study four types of (co)cartesian fibrations of -bicategories over a given base , and prove that they encode the four variance flavors of -inde…
Gray tensor products and lax functors of -categories
Andrea Gagna, Yonatan Harpaz, Edoardo Lanari
We give a definition of the Gray tensor product in the setting of scaled simplicial sets which is associative and forms a left Quillen bifunctor with respect to the bicategorical m…
On a notion of oplax 3-functor
Andrea Gagna
We introduce a notion of normalised oplax -functor suitable for the elementary homotopy theory of strict -categories, following the combinatorics of orientals. We show that a…
On the equivalence of all models for -categories
Andrea Gagna, Yonatan Harpaz, Edoardo Lanari
The goal of this paper is to provide the last equivalence needed in order to identify all known models for -categories. We do this by showing that Verity's model of sat…
Strict n-categories and augmented directed complexes model homotopy types
Andrea Gagna
In this paper we show that both the homotopy category of strict -categories, , and the homotopy category of Steiner's augmented directed complexes…