Related papers: The algebraic structure of the universal complicia…
Simplicial complexes are generalized network structures able to encode interactions occurring between more than two nodes. Simplicial complexes describe a large variety of complex interacting systems ranging from brain networks, to social…
We decribe the correspondence between normalised $\omega$-operads and certain lax monoidal structures on the category of globular sets. As with ordinary monoidal categories, one has a notion of category enriched in a lax monoidal category.…
The relationships between thin elements, commutative shells and connections in cubical omega-categories are explored by a method which does not involve the use of pasting theory or nerves of omega-categories (both of which were previously…
We give a topological description of Ext groups between simple representations of categories via a nerve type construction. We use it to show that the Koszulity of indiscretely based category algebras is equivalent to the locally bouquet…
We introduce a notion of complexity of diagrams (and in particular of objects and morphisms) in an arbitrary category, as well as a notion of complexity of functors between categories equipped with complexity functions. We discuss several…
We introduce necklicial nerve functors from enriched categories to simplicial sets, which include Cordier's homotopy coherent, Lurie's differential graded and Le Grignou's cubical nerves. It is shown that every necklicial nerve can be…
The classifying diagram was defined by Rezk and is a generalization of the nerve of a category; in contrast to the nerve, the classifying diagram of two categories is equivalent if and only if the categories are equivalent. In this paper we…
Abelian groups having partial orderings compatible with their binary operations have long been studied in the literature. In particular, lattice-ordered abelian groups constitute a universal-algebraic variety, and thus form a category which…
Since the time when the first optical instruments have been invented, an idea that the visible image of an object under observation depends on tools of observation became commonly assumed in physics. A way to formalize it in mathematics is…
We investigate models of algebraic theories in the category of cocommutative coalgebras over a field. We establish some of their categorical properties, similar to those of algebraic varieties. We introduce a class of categories of…
In the theory of operads we consider functors of generalized symmetric powers defined by sums of coinvariant modules under actions of symmetric groups. One observes classically that the construction of symmetric functors provides an…
Frobenius algebras in the category of sets and relations ($\mathbf{Rel}$) serve as a unifying framework for various algebraic and combinatorial structures, including groupoids, effect algebras, and abstract circles. Recently, a nerve…
We present a unified framework for categorical systems theory which packages a collection of open systems, their interactions, and their maps into a symmetric monoidal loose right module of systems over a symmetric monoidal double category…
Categorification is the process of finding category-theoretic analogs of set-theoretic concepts by replacing sets with categories, functions with functors, and equations between functions by natural isomorphisms between functors, which in…
A strongly Fregean algebra is an algebra such that the class of its homomorphic images is Fregean and the variety generated by this algebra is congruence modular. To understand the structure of these algebras we study the prime intervals…
The fundamental property of strongly monotone systems, and strongly cooperative systems in particular, is the limit set dichotomy due to Hirsch: if x(0) < y(0), then either omega(x) < omega(y), or omega(x) = omega(y) and both sets consist…
The paper focuses on investigating how certain relations between strict $n$-categories are preserved in a particular implementation of $(\infty,n)$-categories, given by saturated $n$-complicial sets. In this model, we show that the…
We study the complex symmetric structure of weighted composition--differentiation operators of order $n $ on the weighted Bergman spaces $A_{\alpha}^2$ with respect to some conjugations. Then we provide some examples of these operators.
We show the equivalence of two kinds of strict multiple category, namely the well known globular omega-categories, and the cubical omega-categories with connections.
This article considers proximal planar shapes in terms of the proximity of shape nerves and shape nerve complexes. A shape nerve is collection of 2-simplexes with nonempty intersection on a triangulated shape space. A planar shape is a…