THE CATEGORY OF TOPOLOGICAL OBJECTS

Category of Polygroup Objects

category of polygroup objects

On the Levels of Maps and Topological Realization of Objects in a Triangulated Category

The level of a module over a differential graded algebra measures the number of steps required to build the module in an appropriate triangulated category. Based on this notion, we introduce a new homotopy invariant of spaces over a fixed space, called the level of a map. Moreover we provide a method to compute the invariant for spaces over a K-formal space. This enables us to determine the lev...

The Quillen Model Category of Topological Spaces

We give a complete and careful proof of Quillen’s theorem on the existence of the standard model category structure on the category of topological spaces. We do not assume any familiarity with model categories.

Menger probabilistic normed space is a category topological vector space

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...