Related papers: Weak representations, representations up to homoto…

Let $R$ be a commutative ring with unit. We consider the homotopy theory of the category of spectral sequences of $R$-modules with the class of weak equivalences given by those morphisms inducing a quasi-isomorphism at a certain fixed page.…

Various monoidal categories, including suitable representation categories of vertex operator algebras, admit natural Grothendieck-Verdier duality structures. We recall that such a Grothendieck-Verdier category comes with two tensor products…

The main purpose of this paper is to show that the converse of the known implication weakly action representable implies action accessible is false. In particular we show that both action accessibility, as well as the (at least formally…

Let $G$ be a locally compact abelian group with Pontraygin dual $\widehat{G}$. Suppose $P$ is a closed subsemigroup of $G$ containing the identity element $0$. We assume that $P$ has dense interior and $P$ generates $G$. Let…

A multicategory is what remains of a monoidal category when monoidal product is not available. A weak multicategory means that hom-sets are in fact categories, and in place of usual equations, there are natural isomorphisms, which have to…

This is the second of a series of papers which are devoted to a comprehensive theory of maps between orbifolds. In this paper, we develop a basic machinery for studying homotopy classes of such maps. It contains two parts: (1) the…

For any topological groupoid G and any homomorphism from a locally compact Hausdorff topological group K to G, we construct an associated monodromy group. We prove that Morita equivalent topological groupoids have the same monodromy groups.…

We introduce a new construction, the isotropy groupoid, to organize the orbit data for split $\Gamma$-spaces. We show that equivariant principal $G$-bundles over split $\Gamma$-CW complexes $X$ can be effectively classified by means of…

Weak bimonoids in duoidal categories are introduced. They provide a common generalization of bimonoids in duoidal categories and of weak bimonoids in braided monoidal categories. Under the assumption that idempotent morphisms in the base…

We show how one can associate to a given class of finite type G-structures a classifying Lie algebroid. The corresponding Lie groupoid gives models for the different geometries that one can find in the class, and encodes also the different…

This thesis studies the representation theory and linear structures of $\mathcal{Q}$-manifolds and higher Lie algebroids. We introduce differential graded modules (or for short DG-modules) of $\mathcal{Q}$-manifolds and the equivalent…

We study actions of discrete groups on 2-categories. The motivating examples are actions on the 2-category of representations of finite tensor categories and their relation with the extension theory of tensor categories by groups.…

We show that in a weak globular $\omega$-category, all composition operations are equivalent and commutative for cells with sufficiently degenerate boundary, which can be considered a higher-dimensional generalisation of the Eckmann-Hilton…

An n-category is some sort of algebraic structure consisting of objects, morphisms between objects, 2-morphisms between morphisms, and so on up to n-morphisms, together with various ways of composing them. We survey various concepts of…

A theorem of Siebert asserts that if a sequence of semigroups of probability measures on a Lie group G is weakly convergent to a semigroup of the same type, then the corresponding generating functionals are convergent in the weak operator…

Weak (Hopf) bialgebras are described as (Hopf) bimonoids in appropriate duoidal (also known as 2-monoidal) categories. This interpretation is used to define a category wba of weak bialgebras over a given field. As an application, the "free…

We demonstrate that the notions of derivative representation of a Lie algebra on a vector bundle, of semi-linear representations of a Lie group on a vector bundle, and related concepts, may be understood in terms of representations of Lie…

For a group $G$, a weak Cayley isomorphism is a bijection $f:G \to G$ such that $f(g_1g_2)$ is conjugate to $ f(g_1)f(g_2)$ for all $g_1,g_2 \in G$. They form a group $\mathcal W(G)$ that is the group of symmetries of the weak Cayley table…

Let G be a semi-simple non-compact Lie group with unitary lowest/highest weight representations. We consider explicitly the relation between three types of representations of G: positive energy (unitary lowest weight)representations,…

We define and investigate the concept of the groupoid representation induced by a representation of the isotropy subgroupoid. Groupoids in question are locally compact transitive topological groupoids. We formulate and prove the…