Related papers: Twisted-Product Categorical Bundles
The categorified theories known as "doctrines" specify a category equipped with extra structure, analogous to how ordinary theories specify a set with extra structure. We introduce a new framework for doctrines based on double category…
The algebraic approach to bundles in non-commutative geometry and the definition of quantum real weighted projective spaces are reviewed. Principal U(1)-bundles over quantum real weighted projective spaces are constructed. As the spaces in…
Since categories are graphs with additional "structure", one should start from fuzzy graphs in order to define a theory of fuzzy categories. Thus is makes sense to introduce categories whose morphisms are associated with a plausibility…
In a fibre bundle, natural derivatives of a section are defined as tangent vector fields on the image of a section of the fibre bundle. A local extension to vector fields in the tangent bundle leads to a direct proof of the formula…
We investigate global dynamic feedback stabilization from a topological viewpoint. In particular, we consider the general case of dynamic feedback systems, whereby the total space (which includes the state space of the system and of the…
A graded tensor category over a group $G$ will be called a crossed product tensor category if every homogeneous component has at least one multiplicatively invertible object. Our main result is a description of the crossed product tensor…
We study the algebraic geometry of twisted Higgs bundles of cyclic type along complex curves. These objects, which generalize ordinary cyclic Higgs bundles, can be identified with representations of a cyclic quiver in a twisted category of…
Tangent categories provide an axiomatic approach to key structural aspects of differential geometry that exist not only in the classical category of smooth manifolds but also in algebraic geometry, homological algebra, computer science, and…
For the associative algebra $A(\mathfrak g)$ of an infinite-dimensional Lie algebra $\mathfrak g$, we introduce twisted fiber bundles over arbitrary compact topological spaces. Fibers of such bundles are given by elements of algebraic…
Gaussian graphical models represent the backbone of the statistical toolbox for analyzing continuous multivariate systems. However, due to the intrinsic properties of the multivariate normal distribution, use of this model family may hide…
Tangent categories provide a categorical axiomatization of the tangent bundle. There are many interesting examples and applications of tangent categories in a variety of areas such as differential geometry, algebraic geometry, algebra, and…
We compare two notions of $G$-fiber bundles and $G$-principal bundles in the literature, with an aim to clarify early results in equivariant bundle theory that are needed in current work of equivariant algebraic topology. We also give…
We define the notion of a principal S-bundle where S is a groupoid group bundle and show that there is a one-to-one correspondence between principal S-bundles and elements of a sheaf cohomology group associated to S. We also define the…
We slightly extend the notion of a natural fibre bundle by requiring diffeomorphisms of the base to lift to automorphisms of the bundle only infinitesimally, i.e. at the level of the Lie algebra of vector fields. Spin structures are natural…
We introduce a category of noncommutative bundles. To establish geometry in this category we construct suitable noncommutative differential calculi on these bundles and study their basic properties. Furthermore we define the notion of a…
Contextuality is the failure of "local" probabilistic models to become global ones. In this paper we introduce the notions of \emph{measurable fibre bundles}, \emph{probability fibre bundles}, and \emph{sample fibre bundle} which capture…
The derived category of bounded complexes of coherent sheaves is one of the most important algebraic invariants of a smooth projective variety. An important approach to understand derived categories is to construct full strongly exceptional…
Using cluster tilting theory, we investigate tilting objects in the stable category of vector bundles on a weighted projective line of weight type $(2, 2, 2, 2)$. More precisely, a tilting object consisting of rank-two bundles is…
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,…
Twisted and rope-like assemblies of filamentous molecules are common and vital structural elements in cells and tissue of living organisms. We study the intrinsic frustration occurring in these materials between the two-dimensional…