The BV formalism and its shifted versions in field theory have a nice compatibility with boundary structures. Namely, one such structure in the bulk induces a shifted (possibly degenerate) version on its boundary. I will discuss in particular how to proceed from the BFV structure on a “space” slice in field theory, which describes the symplectic reduction due to constraints), to a shifted structure on its boundary (the corners of space–time), which in turn describes a Poisson algebra (possibly up to homotopy). I will describe a few examples, including, time permitting, general relativity in the coframe formulation.