Related papers: Simplicial nerve of an A-infinity category

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 work, we conclude our study of fibred $\infty$-bicategories by providing a Grothendieck construction in this setting. Given a scaled simplicial set $S$ (which need not be fibrant) we construct a 2-categorical version of Lurie's…

This paper explores the relationship amongst the various simplicial and pseudo-simplicial objects characteristically associated to any bicategory C. It proves the fact that the geometric realizations of all of these possible candidate…

We show that the construction due to Leinster and Weber of a generalized Lawvere theory for a familially representable monad on a (co)presheaf category, and the associated ``nerve'' functor from monad algebras to (co)presheaves, have an…

We give a new construction for rigidifying a quasi-category into a simplicial category, and prove that it is weakly equivalent to the rigidification given by Lurie. Our construction comes from the use of necklaces, which are simplicial sets…

We study (not necessarily connected) Z-graded A-infinity-algebras and their A-infinity-modules. Using the cobar and the bar construction and Quillen's homotopical algebra, we describe the localisation of the category of A-infinity-algebras…

We give a detailed proof of the following fundamental result: the singularity category of a ring is triangle equivalent to the stabilization of its stable module category. The result yields singular equivalences between rings of different…

We describe a category of Feynman graphs and show how it relates to compact symmetric multicategories (coloured modular operads) just as linear orders relate to categories and rooted trees relate to multicategories. More specifically we…

We provide conditions for a category with a fiber functor to be equivalent to the category of representations of a linear differential algebraic group. This generalizes the notion of a neutral Tannakian category used to characterize the…

In this article we generalize the theory of subgroup graphs of subgroups of free groups to finite index subgroups $H$ of finitely generated groups $G$. We study and prove various properties of $H$ in relation to its subgroup graph…

Given a symmetric monoidal $\infty$-category $\mathscr{E}$, compatible with finite colimits, we show that the functor sending a simplicial object in $\mathscr{E}$ to its skeletal filtration is canonically lax symmetric monoidal. This…

We construct a left semi-model category of "marked strict $\infty$-categories" for which the fibrant objects are those whose marked arrows satisfy natural closure properties and are weakly invertible. The canonical model structure on strict…

A tangent category is a category with an endofunctor, called the tangent bundle functor, which is equipped with various natural transformations that capture essential properties of the classical tangent bundle of smooth manifolds. In this…

We consider four categories: the category of diagrams of small categories indexed by a given small category O, the (comma) category of small categories over O, the category of diagrams of simplicial sets indexed by O, and the category of…

The aim of these notes is to introduce the intuition motivating the notion of a "complicial set", a simplicial set with certain marked "thin" simplices that witness a composition relation between the simplices on their boundary. By varying…

We introduce a notion of complexity of diagrams (and in particular of objects and morphisms) in an arbitrary category, as well as a notion of complexity of functors between categories equipped with complexity functions. We discuss several…

In this short note we extend the Exodromy Theorem of arXiv:1807.03281 to a large class of stacks and higher stacks. We accomplish this by extending the Galois category construction to simplicial schemes. We also deduce that the nerve of the…

We determine the singularity category of an arbitrary finite dimensional gentle algebra $\Lambda$. It is a finite product of $n$-cluster categories of type $\mathbb{A}_{1}$. Equivalently, it may be described as the stable module category of…

We introduce the notion of weighted limit in an arbitrary quasi-category, suitably generalizing ordinary limits in a quasi-category, and classical weighted limits in an ordinary category. This is accomplished by generalizing Joyal's…

Any tricategory characteristically has associated various simplicial or pseudo-simplicial objects. This paper explores the relationship amongst three of them: the pseudo-simplicial bicategory so-called Grothendieck nerve of the tricategory,…