Related papers: Morphisms between categorified spin networks
This paper is the first in a series. The main goal of the series is to present a geometric construction of certain remarkable tensor categories arising from quantum groups coresponding to the value of deformation parameter $q$ equal to a…
We define a class of maps between holomorphically embedded null curves which generalize conformal transformations, and can be defined in any complex dimension. In four dimensions, we can also define a similar map between self-dual surfaces,…
An algebraic system is proposed that represent surface cobordisms in thickened surfaces. Module and comodule structures over Frobenius algebras are used for representing essential curves. The proposed structure gives a unified algebraic…
Orbits of automorphism groups of partially ordered sets are not necessarily congruence classes, i.e. images of an order homomorphism. Based on so-called orbit categories a framework of factorisations and unfoldings is developed that…
Scientists, engineers, biologists, and technology specialists universally leverage image segmentation to extract shape ensembles containing many thousands of curves representing patterns in observations and measurements. These large curve…
This short paper examines diagrams describing neural network systems in academic conference proceedings. Many aspects of scholarly communication are controlled, particularly with relation to text and formatting, but often diagrams are not…
We give an explicit description of the set of all factorization structures, or twisting maps, existing between the algebras k^2 and k^2, and classify the resulting algebras up to isomorphism. In the process we relate several different…
In this study, we interpret the notion of homotopy of morphisms in the category of crossed modules in a category $\mathsf{C}$ of groups with operations using the categorical equivalence between crossed modules and internal categories in…
In a previous paper we built a modified Hamiltonian formalism to make possible explicit maps among manifolds. In this paper the modified formalism was generalized. As an application, we have built maps among spaces associated to spinors, as…
Given a chiral algebra, we study modules over an arbitrary power of a curve. We describe this category in three different ways: in terms of factorization, in terms of certain chiral operations and as modules for a lie algebra in a certain…
We give an algorithm to calculate the minimal and maximal genus of the orientable closed surface where a graph $G$ can be embedded. For this, we construct some special branched coverings of the 2-sphere. We apply this algorithm to calculate…
Various approaches and measures from network analysis have been applied to granular and particulate networks to gain insights into their structural, transport, failure-propagation and other systems-level properties. In this article, we…
We give a geometric description of a certain class of epimorphisms between complex reflection groups. We classify these epimorphisms, which can be interpreted as ``morphisms'' between the diagrams symbolizing standard presentations by…
We construct an algorithm for computing the cycle classes of the spin components of a stratum of differentials in the moduli space of stable curves $\overline{\mathcal{M}}_{g,n}$. In addition, we implement it within the Sage package…
A combinatorial code $\mathcal{C}$ is a collection of subsets of $[n]$, or equivalently a set of points in $\{0,1\}^n$. A morphism of codes is a map from one combinatorial code to another such that the coordinates of points in the image can…
We propose a new approach to study the Kronecker coefficients by using the Schur-Weyl duality between the symmetric group and the partition algebra. We explain the limiting behavior and associated bounds in the context of the partition…
In this article, we functorially associate definable sets to $k$-analytic curves, and definable maps to analytic morphisms between them, for a large class of $k$-analytic curves. Given a $k$-analytic curve $X$, our association allows us to…
In this note we give a characterization of the sectional category of a map between rational spaces in terms of its Koszul-Quillen model.
In this paper, we review a method for computing and parameterizing the set of homotopy classes of chain maps between two chain complexes. This is then applied to finding topologically meaningful maps between simplicial complexes, which in…
Schwarz genus $\mathsf{g}(\xi)$ of a fibration $\xi\colon E\to B$ is defined as the minimal integer $n$, such that there exists a cover of $B$ by $n$ open sets that admit partial section to $\xi$. Many important concepts, including…