Related papers: A Note on the Soft Group Category
We develop the Witt group for certain braided monoidal categories with duality. In case of a braided fusion category over an algebraically closed field of characteristic zero, we explicitly describe this structure. We then use this…
We present here definitions and constructions basic for the theory of monoidal and tensor categories. We provide references to the original sources, whenever possible. Group-theoretical categories are used as examples
First of all, we focused soft {\beta}-open sets and soft {\beta}-closed sets over the soft topological space and investigated some properties of them. Secondly, we defined the concepts soft {\beta}-continuity, soft {\beta}-irresolute and…
We obtain explicit formulas for the rational homotopy groups of generalised symmetric spaces, i.e., the homogeneous spaces for which the isotropy subgroup appears as the fixed point group of some finite order automorphism of the group. In…
An equivalent description of a symmetric monoidal category is introduced in which, instead of separate associator and commutator isomorphisms satisfying the usual coherence axioms, we simply have associo-commutator isomorphisms satisfying…
In this paper, we study the structure of a generalized near-group fusion category and classified it when it is slightly degenerate.
Categorical structures and their pseudomaps rarely form locally presentable 2-categories in the sense of Cat-enriched category theory. However, we show that if the categorical structure in question is sufficiently weak (such as the…
We introduce the concept of a soft ditopological space as the "soft generalization" of the concept of a ditopological space as it is defined in the papers by L.M. Brown and co-authors, see e.g. L. M. Brown, R. Erturk, S. Dost,…
Category theory provides a compact method of encoding mathematical structures in a uniform way, thereby enabling the use of general theorems on, for example, equivalence and universal constructions. In this article we develop the method of…
In order to provide a good categorical setting to the many different spaces of fields arising in the description of physical theories, a pedagogical introduction to the categorical notion of smooth sets is provided and some simple…
In this article, by using basic properties of fuzzy soft topology we defined fuzzy soft compactness. We also introduced some basic definitions and theorems of the concept.
The purpose of this paper is to show that the dual notions of elements & distinctions are the basic analytical concepts needed to unpack and analyze morphisms, duality, and universal constructions in the Sets, the category of sets and…
This paper considers the possible underlying multicategories for a symmetric monoidal category, and shows that, up to canonical and coherent isomorphism, there really is only one. As a result, there is a well-defined forgetful functor from…
For a mixing shift of finite type, the associated automorphism group has a rich algebraic structure, and yet we have few criteria to distinguish when two such groups are isomorphic. We introduce a stabilization of the automorphism group,…
We introduce a monoidal category whose morphisms are finite partial orders, with chosen minimal and maximal elements as source and target respectively. After recalling the notion of presentation of a monoidal category by the means of…
The aim of this note is to prove that the set of proper normal subgroups of a group endowed with coarse lower topology is a spectral space.
We introduce a tensor product for symmetric monoidal categories with the following properties. Let SMC denote the 2-category with objects small symmetric monoidal categories, arrows symmetric monoidal functors and 2-cells monoidal natural…
Category theory is a branch of mathematics that provides a formal framework for understanding the relationship between mathematical structures. To this end, a category not only incorporates the data of the desired objects, but also…
We develop category-theoretic framework for universal homogeneous objects, with some applications in the theory of Banach spaces, linear orderings, and in topology of compact spaces.
The goal of the paper is to establish and to investigate a fully faithful embedding of the category of group operads into that of crossed interval groups. For this, we introduce a monoidal structure on the slice of the category of operads…