Related papers: Groupoids in categories with pretopology

In this work we deal with coverings and actions of Lie group- groupoids being a sort of the structured Lie groupoids. Firstly, we define an action of a Lie group-groupoid on some Lie group and the smooth coverings of Lie group-groupoids.…

Let $G$ be a Lie group and $G\to\Aut(G)$ be the canonical group homomorphism induced by the adjoint action of a group on itself. We give an explicit description of a 1-1 correspondence between Morita equivalence classes of, on the one hand,…

Polynomial functors are useful in the theory of data types, where they are often called containers. They are also useful in algebra, combinatorics, topology, and higher category theory, and in this broader perspective the polynomial aspect…

We introduce (continuous) partial category actions on sets (topological spaces) and show that each such action admits a universal globalization. Thereby, we obtain a simultaneous generalization of corresponding results for groups, by…

We study actions of discrete groups on contractible topological spaces in which either (1) all stabilizers lie in the family of subgroups of prime power order or (2) all stabilizers lie in the family of finite subgroups. We compare the…

We study the general theory of Frobenius algebras with group actions. These structures arise when one is studying the algebraic structures associated to a geometry stemming from a physical theory with a global finite gauge group, i.e.…

For groups of a topological origin, such as braid groups and mapping class groups, an important source of interesting and highly non-trivial representations is given by their actions on the twisted homology of associated spaces; these are…

In this note we prove that distributors between groupoids in a Barr-exact category E form the bicategory of relations relative to the comprehensive factorization system in Gpd(E). Revised version.

The aim of this paper is to characterize the notion of internal category (groupoid) in the category of Leibniz algebras and investigate the properties of well-known notions such as covering groupoid and groupoid operations (actions) in this…

Throughout this paper $G$ is a fixed group, and $k$ is a fixed field. All categories are assumed to be $k$-linear. First we give a systematic way to induce $G$-precoverings by adjoint functors using a 2-categorical machinery, which unifies…

Using a suitable notion of principal G-bundle, defined relative to an arbitrary cartesian category, it is shown that principal bundles can be characterised as adjunctions that stably satisfy Frobenius reciprocity. The result extends from G,…

In the present paper we describe the action of (not necessarily line) bundles of finite order on the $K$-functor in terms of classifying spaces. This description might provide with an approach for more general twistings in $K$-theory than…

In this paper we discuss some enlargements of the category of sets with semigroup actions and equivariant functions. We show that these enlarged categories possess two idempotent endofunctors. In the case of groups these enlarged categories…

For a linear algebraic group $G$ over a field $k$, we define an equivariant version of the Voevodsky's motivic cobordism $MGL$. We show that this is an oriented cohomology theory with localization sequence on the category of smooth…

Locality is implemented in an arbitrary category using Grothendieck topologies. We explore how different Grothendieck topologies on one category can be related, and, more general, how functors between categories can preserve them. As…

We find the equivalence groupoid of a~class of $(1+1)$-dimensional second-order evolution equations, which are called generalized potential Burgers equations. This class is related via potentialization with two classes of…

We deal with the symmetries of a (2-term) graded vector space or bundle. Our first theorem shows that they define a (strict) Lie 2-groupoid in a natural way. Our second theorem explores the construction of nerves for Lie 2-categories,…

We establish rigidity for partial transformation groupoids associated with algebraic actions of semigroups: If two such groupoids (satisfying appropriate conditions) are isomorphic, then the globalizations of the initial algebraic actions…

For r at least 3, p at least 2, we classify all actions of the groups Diff^r_c(R) and Diff^r_+(S1) by C^p -diffeomorphisms on the line and on the circle. This is the same as describing all nontrivial group homomorphisms between groups of…

In this paper, we develop a $\times$-homotopy fundamental groupoid for graphs, and show a functorial relationship to the 2-category of graphs. We further explore the fundamental groupoid of graph products and develop a groupoid product…