51 citations · 235 across the 34 of their papers we have counts for
18 papers · 1 filter
Keller sequences of exact -categories
Yonatan Harpaz, Daniel Marlowe
We study a family of fibre-cofibre sequences in the -category of exact -categories, which we call Keller sequences, generalising the notion of Verdier sequences of…
Deformation theory and cotangent complex of dg operads
Yonatan Harpaz, Truong Hoang
In the first part, we give an explicit description of the cotangent complex of differential graded (dg) operads, modeled as an operadic infinitesimal bimodule. This leads to a unif…
Trace methods for stable categories I: The linear approximation of algebraic K-theory
Yonatan Harpaz, Thomas Nikolaus, Victor Saunier
We study algebraic K-theory and topological Hochschild homology in the setting of bimodules over a stable category, a datum we refer to as a laced category. We show that in this se…
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…
On k-invariants for -categories
Yonatan Harpaz, Joost Nuiten, Matan Prasma
Every -category can be approximated by its tower of homotopy -categories. In this paper, we prove that the successive stages of this tower are classified by k-…
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 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…
Lax limits of model categories
Yonatan Harpaz
For a diagram of simplicial combinatorial model categories, we show that the associated lax limit, endowed with the projective model structure, is a presentation of the lax limit o…
Quillen cohomology of -categories
Yonatan Harpaz, Joost Nuiten, Matan Prasma
In this paper we study the homotopy theory of parameterized spectrum objects in the -category of -categories, as well as the Quillen cohomology of an $(\infty,…
The tangent bundle of a model category
Yonatan Harpaz, Joost Nuiten, Matan Prasma
This paper studies the homotopy theory of parameterized spectrum objects in a model category from a global point of view. More precisely, for a model category satisfy…
Ambidexterity and the universality of finite spans
Yonatan Harpaz
Pursuing the notions of ambidexterity and higher semiadditivity as developed by Hopkins and Lurie, we prove that the span -category of -finite spaces is the free -sem…
The abstract cotangent complex and Quillen cohomology of enriched categories
Yonatan Harpaz, Joost Nuiten, Matan Prasma
In his fundamental work, Quillen developed the theory of the cotangent complex as a universal abelian derived invariant, and used it to define and study a canonical form of cohomol…
Tangent categories of algebras over operads
Yonatan Harpaz, Joost Nuiten, Matan Prasma
Associated to a presentable -category and an object is the tangent -category , consisting of parameteriz…
Pro-categories in homotopy theory
Ilan Barnea, Yonatan Harpaz, Geoffroy Horel
The goal of this paper is to prove an equivalence between the model categorical approach to pro-categories, as studied by Isaksen, Schlank and the first author, and the -ca…
An integral model structure and truncation theory for coherent group actions
Yonatan Harpaz, Matan Prasma
In this work we study the homotopy theory of coherent group actions from a global point of view, where we allow both the group and the space acted upon to vary. Using the model of…
The Grothendieck construction for model categories
Yonatan Harpaz, Matan Prasma
The Grothendieck construction is a classical correspondence between diagrams of categories and coCartesian fibrations over the indexing category. In this paper we consider the anal…
Quasi-unital -Categories
Yonatan Harpaz
Inspired by Lurie's theory of quasi-unital algebras we prove an analogous result for -categories. In particular, we show that the unital structure of an -category c…
The Cobordism Hypothesis in Dimension 1
Yonatan Harpaz
In 2009 Lurie published an expository article outlining a proof for a higher version of the cobordism hypothesis conjectured by Baez and Dolan in 1995. In this note we give a proof…