Let k be a field. We show that locally presentable, k-linear categories $${\mathcal {C}}$$ dualizable in the sense identity functor can recovered as $$\coprod _i x_i\otimes f_i$$ for objects $$x_i\in {\mathcal and left adjoints $$f_i$$ from to $$\mathrm {Vect}_k$$ are products of copies . This partially confirms conjecture by Brandenburg, author T. Johnson-Freyd. Motivated this, we also charact...

In this paper we introduce intuitionistic fuzzy contra regular weakly generalized open mappings and intuitionistic fuzzy contra regular weakly generalized closed mappings. We investigate some of their properties.

A combinatorial 2-manifold is called weakly regular if the action of its automorphism group on its vertices is transitive. A combinatorial 2-manifold is called degree-regular if each of its vertices have the same degree. Clearly, a weakly regular combinatorial 2-manifold is degree-regular. In [5], Lutz has classified all the weakly-regular combinatorial 2-manifolds on at most 15 vertices, among...

Finite automata whose computations can be reversed, at any point, by knowing the last k symbols read from the input, for a fixed k, are considered. These devices and their accepted languages are called k-reversible automata and k-reversible languages, respectively. The existence of k-reversible languages which are not (k−1)-reversible is known, for each k > 1. This gives an infinite hierarchy o...

In this paper we introduce R-right (left), L-left (right) cancellative and weakly R(L)-cancellative semigroups and will give some equivalent conditions for completely simple semigroups, (completely) regular right (left) cancellative semigroups, right (left) groups, rectangular groups, rectangular bands, groups and right (left) zero semigroups according to R-right (left), L-left (right) and weak...