in this article, we have shown, for the add-point monad t, thepartial morphism category set*is isomorphic to the kleisli category sett. alsowe have proved that the category, sett, of t-algebras is isomorphic to thecategory set of pointed sets. finally we have established commutative squaresinvolving these categories.

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...

We prove two identities that connect some natural tensor products in the category $\sf{LCS}$ of locally convex spaces with $\sf{Ste}$ stereotype spaces. In particular, we give sufficient conditions under which identity $$ X^\vartriangle\odot Y^\vartriangle\cong (X^\vartriangle\cdot Y^\vartriangle)^\vartriangle\cong (X\cdot Y)^\vartriangle holds, where $\odot$ is injective product $\sf{Ste}$, $\...

Après avoir transféré au cadre différentiable la notion algébrique d’équivalence de groupöıdes, nous montrons que les morphismes de la catégorie de fractions correspondante sont représentés par une unique fraction irréductible (calcul de fractions simplifié) que nous identifions aux morphismes de Connes–Skandalis–Haefliger entre espace de feuilles. Dans cette catégorie de fractions, le groupe f...

In this article, we have shown, for the add-point monad T, thepartial morphism category Set*is isomorphic to the Kleisli category SetT. Alsowe have proved that the category, SetT, of T-algebras is isomorphic to thecategory Set of pointed sets. Finally we have established commutative squaresinvolving these categories.