The theory of factorization algebras, and particularly that of constructible factorization algebras, is expected to be very well behaved. For example, it has long been “known” that the assignment taking a stratified manifold to its category of constructible factorization algebras satisfies gluing, i.e., is itself a sheaf. Unfortunately, this and other related facts about factorization algebras have long been “folklore knowledge”, but with no proofs available.

In this talk I will report on recent work with Eilind Karlsson and Claudia I. Scheimbauer, where we close some of these gaps in the literature, including the aforementioned gluing result.