Algebras over not too little discs

By the introduction of locally constant prefactorization algebras at a fixed scale, we show a mathematical incarnation of the fact that observables at a given scale of a topological field theory propagate to every scale over euclidean spaces. The key is that these prefactorization algebras over ℝ n are equivalent to algebras over the little n-disc operad. For topological field theories with defects, we get analogous results by replacing ℝ n with the spaces modelling corners ℝ p × ℝ q ≥0 . As a toy example in 1d, we quantize, once more, constant Poisson structures.