16 citations · 58 across the 23 of their papers we have counts for
28 papers
Personalising Parametric Audio Effect Recommendation for Vocals from Parameter-only Style Priors
Soumya Sai Vanka, Hayato Yamakawa, Kazunobu Kondo +2
Audio effect recommendation has mostly modelled style through reference audio and audio-domain losses. Because the parameter-to-audio map of parametric effects is many-to-one, such…
About the contractibility of the walking coinductive equivalence
Viktoriya Ozornova, Martina Rovelli, Tashi Walde
We study the marked simplicial set obtained as the Roberts-Street nerve of the walking coinductive equivalence. We show that it is a non-contractible saturated complicial set for w…
Cores and localizations of -categories
Viktoriya Ozornova, Martina Rovelli, Tashi Walde
We consider -categories in the limit via the core or localization functors that forget or invert higher non-invertible arrows, respectively. We compare th…
-categories in context
Viktoriya Ozornova, Martina Rovelli
This note is a contribution written for the second volume of the Encyclopedia of mathematical physics. We give an informal introduction to the notions of an -category a…
Waldhausen's -construction
Viktoriya Ozornova, Martina Rovelli
This note is an expository contribution for a proceedings volume of the workshop "Higher Segal Spaces and their Applications to Algebraic K-theory, Hall Algebras, and Combinatorics…
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…
What is an equivalence in a higher category?
Viktoriya Ozornova, Martina Rovelli
The purpose of this survey is to present in a uniform way the notion of equivalence between strict -categories or -categories, and inside a strict -category o…
Model independence of -categorical nerves
Lyne Moser, Viktoriya Ozornova, Martina Rovelli
For most models of -categories an embedding of the -category of 2-categories into that of -categories has been constructed in the form of a nerve co…
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…
An -categorical pasting theorem
Philip Hackney, Viktoriya Ozornova, Emily Riehl +1
We show that any pasting diagram in any -category has a homotopically unique composite. This is achieved by showing that the free 2-category generated by a pasting sche…
An explicit comparison between -complicial sets and -spaces
Julia E. Bergner, Viktoriya Ozornova, Martina Rovelli
We produce a direct Quillen equivalence between two models of -categories: the complete Segal -spaces due to Rezk and the -complicial sets due to Verity.
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-…
Gray tensor product and saturated -complicial sets
Viktoriya Ozornova, Martina Rovelli, Dominic Verity
We show that the pretensor and tensor products of simplicial sets with marking are compatible with the homotopy theory of saturated -complicial sets (which are a proposed model…
Fundamental pushouts of n-complicial sets
Viktoriya Ozornova, Martina Rovelli
The paper focuses on investigating how certain relations between strict -categories are preserved in a particular implementation of -categories, given by saturated $…
Stable homotopy hypothesis in the Tamsamani model
Lyne Moser, Viktoriya Ozornova, Simona Paoli +2
We prove that symmetric monoidal weak n-groupoids in the Tamsamani model provide a model for stable n-types. Moreover, we recover the classical statement that Picard categories mod…
The Duskin nerve of 2-categories in Joyal's cell category Theta_2
Viktoriya Ozornova, Martina Rovelli
We give an explicit and purely combinatorial description of the Duskin nerve of any (r+1)-point suspension 2-category, and in particular of any 2-category belonging to Joyal's cell…
Nerves of 2-categories and 2-categorification of -categories
Viktoriya Ozornova, Martina Rovelli
We show that the homotopy theory of strict 2-categories embeds in that of -categories in the form of 2-precomplicial sets. More precisely, we construct a nerve-categori…
Comparison of Waldhausen constructions
Julia E. Bergner, Angélica M. Osorno, Viktoriya Ozornova +2
In previous work, we develop a generalized Waldhausen -construction whose input is an augmented stable double Segal space and whose output is a unital 2-Segal space. H…
Rings of modular forms and a splitting of
Lennart Meier, Viktoriya Ozornova
Among topological modular forms with level structure, at the prime is the first example that had not been understood yet. We provide a splitting of at the…
2-Segal objects and the Waldhausen construction
Julia E. Bergner, Angélica M. Osorno, Viktoriya Ozornova +2
In a previous paper, we showed that a discrete version of the -construction gives an equivalence of categories between unital 2-Segal sets and augmented stable double ca…
Model structures for -categories on (pre)stratified simplicial sets and prestratified simplicial spaces
Viktoriya Ozornova, Martina Rovelli
We prove the existence of a model structure on the category of stratified simplicial sets whose fibrant objects are precisely -complicial sets, which are a proposed model for $(…
The edgewise subdivision criterion for 2-Segal objects
Julia E. Bergner, Angélica M. Osorno, Viktoriya Ozornova +2
We show that the edgewise subdivision of a -Segal object is always a Segal object, and furthermore that this property characterizes -Segal objects.
The unit of the total décalage adjunction
Viktoriya Ozornova, Martina Rovelli
We consider the décalage construction and its right adjoint . These functors are induced on the category of simplicial objects valued in any bicomplete cate…
2-Segal sets and the Waldhausen construction
Julia E. Bergner, Angélica M. Osorno, Viktoriya Ozornova +2
It is known by results of Dyckerhoff-Kapranov and of Gálvez--Carrillo-Kock-Tonks that the output of the Waldhausen S.-construction has a unital 2-Segal structure. Here, we prove th…