  We introduce the concept of duality between quantum field theories in the
Batalin-Vilkovisky formalism, which is interpreted either as a BV morphism, the
result of dual BV pushforwards or a combination of both. When a BV morphism
affects only the target space of a given model, we call it T-duality. To
justify this name, we demonstrate how topological aspects of T-duality in
string theory such as the relation between curvature and H-flux or isomorphisms
of Courant algebroids are equivalent to dualities of topological sigma models
in two and three dimensions.
