Related papers: On $K_1$ of an assembler

The present note has three aims. First, to complement the theory of cofibrant generation of algebraic weak factorisation systems (AWFSs) to cover some important examples that are not locally presentable categories. Secondly, to prove that…

This is half an overview article since what we describe here is essentially known. We describe $KK$-theory by generators and relations in a formal sum of formal products of $*$-homomorphisms and some synthetical morphisms. What comes out is…

All rational semisimple braided tensor categories are representation categories of weak quasi Hopf algebras. To proof this result we construct for any given category of this kind a weak quasi tensor functor to the category of finite…

For a positive integer $N$ divisible by $4,5,6,7$ or $9$, let $\mathcal{O}_{1,N}(\mathbb{Q})$ be the ring of weakly holomorphic modular functions for the congruence subgroup $\Gamma_1(N)$ with rational Fourier coefficients. We present…

Let $(R, \mf, k_R)$ be regular local $k$-algebra satisfying the weak Jacobian criterion, such that $k_R/k$ is an algebraic field extension. Let $D_R$ be the ring of $k$-linear differential operators of $R$. We give an explicit decomposition…

Semigroups describing the time evolution of open quantum systems in finite dimensional spaces have generators of a special form, known as Lindblad generators. The simple generators, characterized by only one operator, are analyzed. The…

In this paper, we establish a theorem that proves a condition when an inclusion morphism between simplicial sets becomes a weak homotopy equivalence. Additionally, we present two applications of this result. The first application…

In this paper, we find weak generating sets for a classical W-algebra $\mathcal{W}^k(\mathfrak{g},f)$ when $\mathfrak{g}=\mathfrak{sl}_N$ or $\mathfrak{sl}_{N_1|N_2}$. Furthermore, observing the relation between quantum and classical…

We introduce a notion of "weak model category" which is a weakening of the notion of Quillen model category, still sufficient to define a homotopy category, Quillen adjunctions, Quillen equivalences and most of the usual construction of…

We construct a Quillen model structure on the category of spectral categories, where the weak equivalences are the symmetric spectra analogue of the notion of equivalence of categories.

We give a finite presentation by generators and relations for the group O_n(Z[1/2]) of n-dimensional orthogonal matrices with entries in Z[1/2]. We then obtain a similar presentation for the group of n-dimensional orthogonal matrices of the…

We study a categorical construction called the cobordism category, which associates to each Waldhausen category a simplicial category of cospans. We prove that this construction is homotopy equivalent to Waldhausen's…

Let X be a pointed connected simplicial set with loop group G. The linearisation map in K-theory as defined by Waldhausen uses G-equivariant spaces. This paper gives an alternative description using presheaves of sets and abelian groups on…

Let $C$ be a simply laced generalized Cartan matrix. Given an element $b$ of the generalized braid semigroup related to $C$, we construct a collection of mutation-equivalent quivers with potentials. A quiver with potential in such a…

We study perturbations of Feller generators under `lower order terms' with measurable coefficients. We investigate which properties of the original semigroup -- such as positivity, conservativeness and the Feller property -- are passed to…

This paper develops the foundations of a simplicial theory of weak omega-categories, which builds upon the insights originally expounded by Ross Street in his 1987 paper on oriented simplices. The resulting theory of weak complicial sets…

We extend Goodwillie's classification of finitary linear functors to arbitrary small functors. That is we show that every small linear simplicial functor from spectra to simplicial sets is weakly equivalent to a filtered colimit of…

We construct a cofibrantly generated Quillen model structure on the category of small differential graded categories. ----- Nous construisons une structure de categorie de modeles de Quillen a engendrement cofibrant sur la categorie des…

We produce a cofibrantly generated simplicial symmetric monoidal model structure for the category of (small unital) C*-categories, whose weak equivalences are the unitary equivalences. The closed monoidal structure consists of the maximal…

In this paper the concept of compatible weak factorization systems in general categories is introduced as a counterpart of compatible complete cotorsion pairs in abelian categories. We describe a method to construct model structures on…