New preprints

New preprints

[Olivia Caramello]

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



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