The coherent homotopy category over a fixed space is a category of fractions

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...

Homotopy Coherent Category Theory

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...

A Coherent Homotopy Category of 2-track Commutative Cubes

We consider a category H ⊗ (the homotopy category of homotopy squares) whose objects are homotopy commutative squares of spaces and whose morphisms are cubical diagrams subject to a coherent homotopy relation. The main result characterises the isomorphisms of H ⊗ to be the cube morphisms whose forward arrows are homotopy equivalences. As a first application of the new category we give a direct ...

Homotopy Representations over the Orbit Category

Let G be a finite group. The unit sphere in a finitedimensional orthogonal G-representation motivates the definition of homotopy representations, due to tom Dieck. We introduce an algebraic analogue and establish its basic properties, including the Borel–Smith conditions and realization by finite G-CW-complexes.