MV-algebras as sheaves of ℓ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\ell $$\end{document}-groups on fuzzy topological spaces

We introduce the concept of fuzzy sheaf as a natural generalization of a sheaf over a topological space in the context of fuzzy topologies. Then, we prove a representation for a class of MV-algebras that we called “locally retractive,” in which the representing object is an MV-sheaf of lattice-ordered Abelian groups, namely a fuzzy sheaf in which the base (fuzzy) topological space is an MV-topological space and the stalks are Abelian ℓ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\ell $$\end{document}-groups. Last, we show that any MV-algebra is embeddable in a locally retractive algebra and, therefore, in the algebra of global sections of one of such sheaves.