Dear All, The following preprints are available from the Mathematics ArXiv. O. Caramello, "Extensions of flat functors and theories of presheaf type" Abstract: We develop a general theory of extensions of flat functors along geometric morphisms of toposes, and apply it to the study of the class of theories whose classifying topos is equivalent to a presheaf topos. As a result, we obtain a characterization theorem providing necessary and sufficient semantic conditions for a theory to be of presheaf type. This theorem subsumes all the previous partial results obtained on the subject and has several corollaries which can be used in practice for testing whether a given theory is of presheaf type as well as for generating new examples of theories belonging to this class. Along the way, we establish a number of other results of independent interest, including developments about colimits in the context of indexed categories, expansions of geometric theories and methods for constructing theories classified by a given presheaf topos. http://arxiv.org/abs/1404.4610 (158 pages) O. Caramello and A. C. Russo, "The Morita-equivalence between MV-algebras and abelian l-groups with strong unit" Abstract: We show that the theory of MV-algebras is Morita-equivalent to that of abelian l-groups with strong unit. This generalizes the well-known equivalence between the categories of set-based models of the two theories established by D. Mundici in 1986, and allows to transfer properties and results across them by using the methods of topos theory. We discuss several applications, including a sheaf-theoretic version of Mundici's equivalence and a bijective correspondence between the geometric theory extensions of the two theories. http://arxiv.org/abs/1312.1272 (29 pages) Links to video-recordings of talks in French about these two papers are available at the address http://www.oliviacaramello.com/Videos/Videos.htm . Best regards, Olivia Caramello [For admin and other information see: http://www.mta.ca/~cat-dist/ ]