Pullbacks of Leavitt path algebras from pushouts of graphs

To a directed graph one can assign its Leavitt path algebra, which is a quotient of the path algebra of the extended graph by a certain ideal. An appropriate choice of morphisms in a category whose objects are directed graphs makes this assignment into a covariant functor into the category of algebras. In spite of the apparent covariant nature of the construction of Leavitt path algebras, we prove that, for a suitable class of graphs, pushouts of directed graphs give rise to pullbacks of the underlying Leavitt path algebras. This talk is based on the joint work with Piotr M. Hajac and Sarah Reznikoff.