Related papers: Model independence of $(\infty,2)$-categorical ner…

Our aim is to compare three nerve functors for strict $n$-categories: the Street nerve, the cellular nerve and the multi-simplicial nerve. We show that these three functors are equivalent in some appropriate sense. In particular, the…

We set the foundations of a theory of Grothendieck $(\infty,2)$-topoi based on the notion of fibrational descent, which axiomatizes both the existence of a classifying object for fibrations internal to an $(\infty,2)$-category as well as…

In this work, we introduce a 2-categorical variant of Lurie's relative nerve functor. We prove that it defines a right Quillen equivalence which, upon passage to $\infty$-categorical localizations, corresponds to Lurie's scaled…

In this paper we introduce a functor, called the simplicial nerve of an A-infinity category, defined on the category of (small) A-infinity categories with values in simplicial sets. We prove that the simplicial nerve of any A-infinity…

We develop the theory of categories of measurable fields of Hilbert spaces and bounded fields of bounded operators. We examine classes of functors and natural transformations with good measure theoretic properties, providing in the end a…

In this note we consider partial model categories, by which we mean relative categories that satisfy a weakened version of the model category axioms involving only the weak equivalences. More precisely, a partial model category will be a…

We describe several equivalent models for the infinity-category of infinity-local systems of chain complexes over a space using the framework of quasi-categories. We prove that the given models are equivalent as infinity-categories by…

In this article we provide a model-independent definition of the concept of lax $2$-functors from $(\infty,2)$-category theory and show that it agrees with the existing and widely used combinatorial model for those in terms of…

The classifying diagram was defined by Rezk and is a generalization of the nerve of a category; in contrast to the nerve, the classifying diagram of two categories is equivalent if and only if the categories are equivalent. In this paper we…

We study 2-representations of finitary 2-categories with involution and adjunctions by functors on module categories over finite dimensional algebras. In particular, we define, construct and describe in detail (right) cell 2-representations…

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 $(\infty,n)$-category and $(\infty,n)$-functor, discussing some of the different…

We show that the Yoneda embedding 'is' $(\infty,2)$-natural with respect to the functoriality of presheaves via left Kan extension, refining the $(\infty,1)$-categorical result proven independently by Haugseng-Hebestreit-Linskens-Nuiten and…

We propose a framework for producing interesting subcategories of the category ${}_A\mathsf{Mod}$ of left $A$-modules, where $A$ is an associative algebra over a field $k$. The construction is based on the composition, $Y$, of the Yoneda…

Let A be an algebra with a countable basis and let B be, say, a Frechet algebra that contains A as a dense subalgebra. This embedding induces a functor from the derived category of B-modules to the derived category of A-modules. In many…

We develop the Morita theory of fusion 2-categories. In order to do so, we begin by proving that the relative tensor product of modules over a separable algebra in a fusion 2-category exists. We use this result to construct the Morita…

We extend the framework of combinatorial model categories, so that the category of small presheaves over large indexing categories and ind-categories would be embraced by the new machinery called class-combinatorial model categories. The…

The bicategorical point of view provides a natural setting for many concepts in the representation theory of monoidal categories. We show that centers of twisted bimodule categories correspond to categories of 2-dimensional natural…

We axiomatically define (pre-)Hilbert categories. The axioms resemble those for monoidal Abelian categories with the addition of an involutive functor. We then prove embedding theorems: any locally small pre-Hilbert category whose monoidal…

We study limits in 2-categories whose objects are categories with extra structure and whose morphisms are functors preserving the structure only up to a coherent comparison map, which may or may not be required to be invertible. This is…

We give an explicit description for the nerve of crossed module of categories.