  I discuss how Alain Badiou's Logics of Worlds attempts to rephrase his
material dialectic philosophical project in terms of topos theory. It turns out
that his account restricts to the so called local topos theory. In particular,
his claim that categorical change is not genuine is based on a constrained
understanding of topos theory. We then discuss his own 'postulate of
materialism' and demonstrate that it has two different interpretations
depending on whether it is articulated in local or elementary topos theory.
While the main concerns in this paper are technical, we also address the
serious consequences of topos theory that weigh Badiou's philosophical project.
