We associate a diagrammatic monoidal category $\mathcal{H}\textit{eis}_k(A;z,t)$, which we call the quantum Frobenius Heisenberg category, to symmetric superalgebra $A$, central charge $k \in \mathbb{Z}$, and invertible parameters $z,t$ in some ground ring. When $A$ is trivial, i.e. it equals ring, these categories recover introduced our previous work, when $k$ zero they yield generalizations o...

The notion of exterior space consists of a topological space together with a certain nonempty family of open subsets that is thought of as a ‘system of open neighborhoods at infinity’ while an exterior map is a continuous map which is ‘continuous at infinity’. The category of spaces and proper maps is a subcategory of the category of exterior spaces. In this paper we show that the category of e...

We introduce a quantale-valued generalization of approach spaces in terms of quantale-valued gauges. The resulting category is shown to be topological and to possess an initially dense object. Moreover we show that the category of quantale-valued approach spaces defined recently in terms of quantale-valued closures is a coreflective subcategory of our category and, for certain choices of the qu...

In this paper, we formalize the Menger probabilistic normed space as a category in which its objects are the Menger probabilistic normed spaces and its morphisms are fuzzy continuous operators. Then, we show that the category of probabilistic normed spaces is isomorphicly a subcategory of the category of topological vector spaces. So, we can easily apply the results of topological vector spaces...

Let X be a scheme, and let G be an affine group scheme acting on X. Under reasonable hypotheses on X and G, we construct a t-structure on the derived category of G-equivariant coherent sheaves that in many ways resembles the perverse coherent t-structure, but which incorporates additional information from the G-action. Under certain circumstances, the heart of this t-structure, called the “stag...

The present paper has been an attempt to investigate the general fuzzy automata on the basis of complete residuated lattice-valued ($L$-GFAs). The study has been chiefly inspired from the work by Mockor cite{15, 16, 17}. Regarding this, the categorical issue of $L$-GFAs has been studied in more details. The main issues addressed in this research include: (1) investigating the relationship betwe...

A study was conducted to evaluate the correlation between selected physico-chemical parameters of water and their effects on growth of Rainbow trout (Oncorhynchus mykiss) in raceway system in the area of Sarab Gerdu, Iran. The samples were collected from twenty raceways (270- day old fish, surface area 55m2 flow rate 150 ls-1 total production 15 T). Physico-chemical parameters were the fluctuat...