T-duality through BV Morphisms and BV Pushforwards in Topological Field Theories

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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.